Question 12 Marks
$x(a - 3) + y(3 - a)$
Answer$= x(a - 3) - y(a - 3) $
$= (a - 3)(x - y)$
View full question & answer→Question 22 Marks
Factorise:
$=a b\left(x^2+y^2\right)-x y\left(a^2-b^2\right)$
Answer$=a b\left(x^2+y^2\right)-x y\left(a^2-b^2\right)$
$=a b x^2+a b y^2+x y a^2-x y b^2$
$=a b x^2-x y a^2-x y b^2+a b y^2$
$=a x(b x-a y)-b y(b x-a y)$
$=(b x-a y)(a x-b y)$
View full question & answer→Question 32 Marks
Factorise:
$16 x^5-144 x^3$
Answer$16 x^5-144 x^3$
$=16 x^3\left[x^2-9\right]$
$=16 x^3\left[(x)^2-(3)^2\right]$
$=16 x^3(x+3)(x-3)$
View full question & answer→Question 42 Marks
Factorise: $16(2 p-3 q)^2-4(2 p-3 q)$
Answer$16(2 p-3 q)^2-4(2 p-3 q)$
$=(2 p-3 q)\{16(2 p-3 q)-4\}$
$=(2 p-3 q)(32 p-48 q-4)$
$=4(2 p-3 q)(8 p-12 q-1)$
View full question & answer→Question 52 Marks
Factorise:
$(x-2 y)^2+4 x-8 y$
Answer$(x-2 y)^2+4 x-8 y$
$=(x-2 y)^2+4(x-2 y)$
$=(x-2 y)(x-2 y+4)$
View full question & answer→Question 62 Marks
Factorise: $ar + br + at + bt$
Answer$ar + br + at + bt $
$= r(a + b)+ t(a + b)$
$= (a + b)(r + t)$
View full question & answer→Question 72 Marks
Factorise:
$3m^2+ 24m + 36$
Answer$ 3 m^2+24 m+36 $
$ =3\left(m^2+8 m+12\right) $
$ =3\left(m^2+6 m+2 m+12\right) $
$ \{12=6 \times 2,8=6+2\} $
$ =33(m+6)+(m+2) $
$ =(2 x-3)(3 x+2) $
View full question & answer→Question 82 Marks
Factorise:
$a b\left(x^2+y^2\right)-x y\left(a^2+b^2\right)$
Answer$a b\left(x^2+y^2\right)-x y\left(a^2+b^2\right)$
$=a b x^2+a b y^2+x y a^2-x y b^2$
$=a b x^2-x y a^2-x y b^2+a b y^2$
$=a x(b x-a y)-b y(b x-a y)$
$=(b x-a y)(a x-b y)$
View full question & answer→Question 92 Marks
Factorise:
$ x^2+8 x+16 $
Answer$ x^2+8 x+16 $
$ =(x)^2+2 \times x \times 4+(4)^2 $
$ =(x+4)^2 $
View full question & answer→Question 102 Marks
$(3 x-4 y)^2-25 z^2$
Answer$(3 x-4 y)^2-25 z^2$
$=(3 x-4 y)^2-(5 z)^2$
$=(3 x-4 y+5 z)(3 x-4 y-5 z)$
View full question & answer→Question 112 Marks
Factorise:
$x^2-17 x+16$
Answer$x^2-17 x+16$
$ =x^2-x-16 x+16 $
$ \{16=(-1) \times(-16), 17=-1-16\} $
$ =x(x-1)-16(x-1) $
$ =(x-1)(x-16) $
View full question & answer→Question 122 Marks
Factorise:
$x^2-x(a+2 b)+2 a b$
Answer$x^2-x(a+2 b)+2 a b$
$=x^2-x a-2 b x+2 a b$
$= x(x - a) - 2bx + 2ab$
$ = x(x - a) - 2b(x - a) $
$= (x - a)(x - 2b)$
View full question & answer→Question 132 Marks
Factorise:
$x^2-5 x-24$
Answer$x^2-5 x-24$
$=x^2-8 x+3 x-24$
${-24 = -8 × 3, -5 = -8 + 3}$
$= x(x - 8) + 3(x - 8)$
$= (x - 8)(x + 3)$
View full question & answer→Question 142 Marks
Factorise:$49 a^2+84 a b+36 b^2 $
Answer$49 a^2+84 a b+36 b^2 $
$ =(7 a)^2+2 \times 7 a \times 6 b+(6 b)^2$
$\{\because$ $a^2+ 2ab + b^2= (a + b)^2\}$
$= (7a + 6b)^2$
View full question & answer→Question 152 Marks
Factorise:
$4 x^2-9 y^2$
Answer$4 x^2-9 y^2$
$=(2 x)^2-(3 y)^2$
$=(2 x+3 y)(2 x-3 y)$
$\{\because a^2- b^2= (a + b)(a - b)\}$
View full question & answer→Question 162 Marks
Factorise: $(x + y)(2x + 5) - (x + y)(x + 3)$
Answer$(x + y)(2x + 5) - (x + y)(x + 3) $
$= (x + y)(2 + 5 - x - 3) $
$= (x + y)(x + 2)$
View full question & answer→Question 172 Marks
Factorise:
$ 4 y^2+20 y+25 $
Answer$ 4 y^2+20 y+25 $
$=(2 y)^2+2 \times 2 y \times 5+(5)^2 $
$=\left(2 y^2+5\right)^2 $
$\left\{\therefore a^2+2 a b+b=(a+b)^2\right\} $
View full question & answer→Question 182 Marks
Factorise: $20 a^2-45 b^2$
AnswerUsing: $a^2-b^2=(a+b)(a-b) $
$20 a^2-45 b^2$
$=5\left(4 a^2-9 b^2\right)$
$=5(2 a)^2-(3 b)^2$
$=5(2 a+3 b)(2 a-3 b)$
View full question & answer→Question 192 Marks
$(2x + 5y)2 - 1$
Answer$(2x + 5y)2 - 1$
$= (2x + 5y + 1)(2x + 5y - 1)$
$\{\because a2 - b2 = (a + b)(a - b) \}$
View full question & answer→Question 202 Marks
Factorise:
$2 a+6 b-3(a+3 b)^2$
Answer$2 a+6 b-3(a+3 b)^2$
$=2(a+3 b)-3(a+3 b)^2$
$=(a+3 b)\{2-3(a+3 b)\}$
$=(a+3 b)(2-3 a-9 b)$
View full question & answer→Question 212 Marks
Evalute: $ \left\{(405)^2-(395)^2\right\} $
Answer$ \left\{(405)^2-(395)^2\right\} $
$ (405)^2-(395)^2 $
$ =(405+395)(405-395) $
$ \left\{\because a^2-b^2(a+b)(a-b)\right\} $
$ =800 \times 10=8000 $
View full question & answer→Question 222 Marks
Factorise:
$6 a b-b^2+12 a c-2 b c$
Answer$6 a b-b^2+12 a c-2 b c$
$=6 a b+12 a c-b^2-2 b c$
$=6 a(b+2 c)-b(b+2 c)$
$= (b + 2c)(6a - b)$
View full question & answer→Question 232 Marks
Factorise: $y^2+y-72$
Answer$y^2+y-72$
$=y^2+9 y-8 y-72$
$\{-72=9 \times(-8), 1=9-8\}$
$= y(y + 9) - 8(y + 9) $
$= (y + 9)(y - 8)$
View full question & answer→Question 242 Marks
Factorise: $ (2 a+3 b)^2-16 c^2$
Answer$ (2 a+3 b)^2-16 c^2$
$ =(2 a+3 b) 2-(4 c)^2 $
$ =(2 a+3 b+4 c)(2 a+3 b-4 c) $
$ \{\because a 2-b 2=(a+b)(a-b)\} $
View full question & answer→Question 252 Marks
Factorise:
$p^2-6 p-16$
Answer$p^2-6 p-16$
$=p^2+8 p-2 p-16$
$\{-16=8 \times(-2), 6=8-2\}$
$= p(p + 8) - 2(p + 8)$
$ = (p + 8)(p - 2)$
View full question & answer→Question 262 Marks
Factorise:
$x^2-23 x+42$
Answer$x^2-23 x+42$
$=x^2-2 x-21 x+42$
$\{42=(-2) \times(-21),-23=-2-21\}$
$= x(x - 2) - 21(x - 2) $
$= (x - 2)(x - 21)$
View full question & answer→Question 272 Marks
Factorise: $ x^2+6 a x+9 a^2$
Answer$ x^2+6 a x+9 a^2$
$=(x)^2+2 \times x \times 3 a+(3 a)^2 $
$ =(x+3 a)^2 $
View full question & answer→Question 282 Marks
Factorise: $x^2+x-132$
Answer$x^2+x-132$
$=x^2+12 x-11 x-132$
${-132 = 12 × (-11), 1 = 12 - 11}$
$= x(x + 12) - 11(x + 12) $
$= (x + 12)(x - 11)$
View full question & answer→Question 292 Marks
Factorise: $1 - (b - c)^2$
Answer$1 - (b - c)^2$
$= (1)^2 - (b - c)^2$
$= (1 + b + c)(1 - b + c)$
$\{\because a^2- b^2= (a + b)(a - b)\}$
View full question & answer→Question 302 Marks
Factorise: $9a^2b - 25$
AnswerUsing: $a^2-b^2=(a+b)(a-b)$
$=(3 a b)^2-(5)^2$
$=(3 a b+5)(3 a b-5)$
View full question & answer→Question 312 Marks
Factorise: $x^2- 7x - 30$
Answer$x^2-7 x-30$
$=x^2-10 x+3 x-30$
${-30 = -10 × 3, -7 = -10 + 3}$
$= x(x - 10) + 3(x - 10) $
$= (x - 10)(x + 3)$
View full question & answer→Question 322 Marks
Factorise: $4a^2- 9$
Answer$4a^2- 9$
$= (2a)^2- (3)^2$
$= (2a + 3)(2a - 3)$ $\{\therefore a^2- b^2= (a + b)(a - b)\}$
View full question & answer→Question 332 Marks
Factorise: $y^2+19 y+60$
Answer$y^2+19 y+60$
$=y^2+19 y+60$
${60 = 15 × 4, 19 = 15 + 4}$
$= y(y + 15) + 4(y + 15)$
$= (x + 15)(x + 4)$
View full question & answer→Question 342 Marks
Factorise: $63 a^2-112 b^2=7$
AnswerUsing: $a^2-b^2=(a+b)(a-b) $
$63 a^2-112 b^2=7$
$\left(9 a^2-16 b^2\right)$
$=7 [(3 a)^2-(4 b)^2]$
$=7(3 a+4 b)(3 a-4 b).$
View full question & answer→Question 352 Marks
Factorise: $1-6 x+9 x^2$
Answer$1-6 x+9 x^2$
$=(1)^2-2 \times 1 \times 3 x+(3 x)^2$
$=(1-3 x)^2$
$\{\because a2 - 2ab + b2 = (a - b)2\}$
View full question & answer→Question 362 Marks
Factorise: $q^2-10 q+21$
Answer$q^2-10 q+21$
$=q^2+7 q-3 q+21$
${21 = (-7) × (-3), -10 = -7 - 3}$
$= q(q - 7) - 3(q - 7)$
$ = (q - 7)(q - 3)$
View full question & answer→Question 372 Marks
Factorise: $6 p^2+11 p-10$
Answer$6 p^2+11 p-10$
$=6 x^2+15 x-4 x-10$
${6 × (-10) = 60, -60 = 15 × (-4), 11 = 15 - 4}$
$= 3x(2x + 5) - 2(2x + 5) $
$= (3x - 2)(2x + 5)$
View full question & answer→Question 382 Marks
Factorise: $3 x^2+10 x+8$
Answer$3 x^2+10 x+8$
$=3 x^2+6 x+4 x+8$
${24 = 3 × 8, 24 = 6 × 4, 10 = 6 + 4}$
$= 3x(x + 2) + 4(x + 2) $
$= (x + 2)(3x + 4)$
View full question & answer→Question 392 Marks
Factorise: $28-31 x-5 x^2$
Answer$28-31 x-5 x^2$
$=28-35 x+4 x-5 x^2$
${28 × (-5) = -140, -140 = -35 × 4, -31 = -35 + 4}$
$= 7(4 - 5x) + x(4 - 5x)$
$= (4 - 5x)(7 + x)$
View full question & answer→Question 402 Marks
Factorise:
$ 1+2 x+x^2$
Answer$ 1+2 x+x^2$
$=(1)^2+2 \times 1 \times x+(x)^2 $
$ =(1+x)^2 $
View full question & answer→Question 412 Marks
Factorise: $a^2 b^2-6 a b c+9 c^2$
Answer$a^2 b^2-6 a b c+9 c^2$
$=(a b)^2-2 \times a b \times 3 c+(3 c)^2$
$=(a b-3 c)^2$
View full question & answer→Question 422 Marks
Factorise: $y^2+10 y+24$
Answer$y^2+10 y+24$
$=y^2+6 y+4 y+24$
$ {24 = 6 × 4, 10 = 6 + 4} $
$= y(y + 6) + 4(y + 6) $
$= (y + 6)(y + 4)$
View full question & answer→Question 432 Marks
Factorise: $m^2+2 m^2 n^2+n^4$
Answer$m^2+2 m^2 n^2+n^4$
$=\left(m^2\right)^2+2 m^2 n^2+\left(n^2\right)^2$
$=\left(m^2+n^2\right)^2$
$\{\because a^2+ 2ab + b^2= (a + b)^2\}$
View full question & answer→Question 442 Marks
Factorise: $2 x^2+x-45$
Answer$2 x^2+x-45$
$=2 x^2+10 x-9 x-45$
${2 × (-45) = -90, -90 = (10) × (-9), 1 = 10 - 9}$
$= 2x(x - 5) + 9(x - 5) $
$= (x - 5)(2x + 9)$
View full question & answer→Question 452 Marks
Factorise: $9 a^2-b^2+4 b-4$
Answer$9 a^2-b^2+4 b-4$
$=9 a^2-\left(b^2-4 b+4\right)$
$=(3 a)^2-[(b)^2-2 \times b \times 2+(2)^2$
$=(3 a)^2-(b-2)^2.$
$\{\because a^2- 2ab + b^2= (a - b)^2\}$
$= (3a + b - 2)(3a - b + 2)$
$\{\because a^2- b^2= (a + b)(a - b)\}$
View full question & answer→Question 462 Marks
Factorise: $7 x^2-19 x-6$
Answer$7 x^2-19 x-6$
$=7 x^2-21 x+2 x-6$
${7 × (-6) = -42, -42 = -21 × 2, -19 = -21 + 2}$
$= 7x(x - 3) + 2(x - 3) $
$= (x - 3)(7x + 2)$
View full question & answer→Question 472 Marks
Factorise: $p^2-4 p-11$
Answer$p^2-4 p-11$
$=p^2+11 p-7 p-77$
${-77 = -11 × 7, -4 = -11 + 7}$
$= p(p - 11) + 7(p - 11) $
$= (p - 11)(p + 7)$
View full question & answer→Question 482 Marks
Factorise: $(l+3)^2-(l-m)^2$
Answer$(l+3)^2-(l-m)^2$
$= (l + m + l - m)(l + m - l + m)$
$\{\because a2 - b2 = (a + b)(a - b)\}$
$= 2l × 2m = 4lm$
View full question & answer→Question 492 Marks
Factorise: $x^2-10 x+24$
Answer$x^2-10 x+24$
$=x^2-6 x-4 x+24$
${24 = (-6) × (-4), -10 = -6 - 4}$
$= x(x - 6) - 4(x - 6) $
$= (x - 6)(x - 4)$
View full question & answer→Question 502 Marks
Factorise: $81-49 \mathrm{x}^2$
Answer$81-49 \mathrm{x}^2$
$=(9)^2-(7 \mathrm{x})^2=(9+7 \mathrm{x})(9-7 \mathrm{x})$
$\{\because a^2- b^2= (a + b)(a - b)\}$
View full question & answer→Question 512 Marks
Factorise: $16 x^2-24 x+9$
Answer$16 x^2-24 x+9$
$=(4 x)^2-2 \times 4 x \times 3+(3)^2$
$=(4 x-3)^2$
View full question & answer→Question 522 Marks
Factorise: $ab^2+ (a - 1)b - 1$
Answer$= ab^2+ ab - b - 1$
$= ab(b + 1) - 1(b + 1)$
$= (b + 1)(ab - 1)$
View full question & answer→Question 532 Marks
Evalute: ${(7.8)^2- (2.2)^2}$
Answer$(7.8)^2- (2.2)^2$
$= (7.8 + 2.2)(7.8 - 2.2)$
$= 10.00 × 5.6$
$= 56$
View full question & answer→Question 542 Marks
Factorise: $x^2- xz + xy - yz$
Answer$(x-2 y)^2+4 x-8 y$
$=(x-2 y)^2+4(x-2 y)$
$=(x-2 y)(x-2 y+4)$
View full question & answer→Question 552 Marks
Factorise: $a^2+6 a-91$
Answer$a^2+6 a-91$
$=a^2+13 a-7 a-91$
${-91 = 13 × (-7), 6 = 13 - 7}$
$= a(a + 13) - 7(a + 13)$
$ = (a + 13)(a - 7)$
View full question & answer→Question 562 Marks
Factorise: $x^2+13 x+40$
Answer$x^2+13 x+40$
$=x^2+5 x+8 x+40$
${40 = 5 × 8, 13 = 5 + 8}$
$= x(x + 5) + 8(y + 5) $
$= (x + 5)(x + 8)$
View full question & answer→Question 572 Marks
Factorise: $x^2-22 x+117$
Answer$x^2-22 x+117$
$=x^2-13 x-9 x+117$
${117 = (-13) × (-9), -22 = -13 - 9}$
$= x(x - 13) - 9(y - 13) $
$= (x - 9)(x - 13)$
View full question & answer→Question 582 Marks
Factorise: $m^2-4 m n+4 n^2$
Answer$m^2-4 m n+4 n^2$
$=(m)^2-2 \times m \times 2 n+(2 n)^2$
$=(m-2 n)^2$
View full question & answer→Question 592 Marks
Factorise: $4 n^2-8 n+3$
Answer$4 n^2-8 n+3$
$=4 n^2-6 n-2 n+3$
${4 × 3 = 12, 12 = (-6) × (-2), - 8 = -6 - 2}$
$= 2n(2n - 3) - 1(2n - 3)$
$ = (2n - 3)(2n - 1)$
View full question & answer→Question 602 Marks
Factorise: $(l+m)^2-41 m$
Answer$(l+m)^2-41 m$
$=l^2+m^2+21 m-41 m$
$=l^2+m^2-21 m=l^2-21 m+m^2$
$=(l-m)^2$
$\{\because a^2+ 2ab + b^2= (a + b)^2\}$
View full question & answer→Question 612 Marks
Factorise: $9+6 z+z^2$
Answer$9+6 z+z^2$
$=(3)^2+2 \times 3 \times z+(z)^2 $
$ =(3+z)^2 $
View full question & answer→Question 622 Marks
Factorise: $z^2-12 z-45$
Answer$z^2-12 z-45$
$=z^2-15 z+3 z-45$
${-45 = -15 × 3, -12 = -15 + 3}$
$= z(z - 15) + 3(z - 15) $
$= (z - 15)(z + 3)$
View full question & answer→Question 632 Marks
Factorise:
$=y^2-x y(1-x)-x^3$
Answer$=y^2-x y(1-x)-x^3$
$=y^2-x y+x^2 y-x^2$
$=y(y-x)+x^2(y-x)$
$=(y-x)\left(y+x^2\right)$
View full question & answer→Question 642 Marks
Factorise: $y^2-6 y-135$
Answer$y^2-6 y-135$
$=y^2-15+9 y-135$
${-135 = -15 × 9, -6 = -15 + 9}$
$= y(y - 15) + 9(y - 15)$
$= (y - 15)(y + 9)$
View full question & answer→Question 652 Marks
Factorise: $3 z^2-10 z+8$
Answer$3 z^2-10 z+8$
$=3 z^2-6 z-4 z+8$
$\{24 = 3 × 8, 24 = (-6) × (-4), -10 = -6 - 4\}$
$= 3z(z - 2) - 4(z - 2) $
$= (z - 2)(3z - 4)$
View full question & answer→Question 662 Marks
Factorise: $ 9 y^2-12 y+4$
Answer$ 9 y^2-12 y+4$
$=(3 y)^2-2 \times 3 y \times 2+(2)^2 $
$\{\because a 2-2 a b+b 2=(a-b) 2\}$
$ =(3 y-2)^2$
View full question & answer→Question 672 Marks
Factorise: $3 y^2+14 y+8$
Answer$3 y^2+14 y+8$
$=3 y^2+12 y+2 y+8$
${24 = 3 × 8, 24 = 12 × 2, 14 = 12 + 2}$
$= 3y(y + 4) + 2(y + 4) $
$= (y + 4)(3y + 2)$
View full question & answer→Question 682 Marks
Factorise: $a b^2-b c^2-a b+c^2 $
Answer$a b^2-b c^2-a b+c^2 $
$a b^2-a b-b c^2+c^2$
$=a b(b-1)-c^2(b-1)$
$=(b-1)\left(a b-c^2\right)$
View full question & answer→Question 692 Marks
Factorise: $(x+5)^2-4(x+5)$
Answer$(x+5)^2-4(x+5)$
$= (x + 5)(x + 5 - 4) $
$= (x + 5)(x + 1)$
View full question & answer→Question 702 Marks
Factorise: $x^2- ax - bx + ab$
Answer$x^2- ax - bx + ab$
$= x(x - a) - b(x - a)$
$ = (x - a)(x - b)$
View full question & answer→Question 712 Marks
Factorise: $36 a^2+36 a+9$
Answer$36 a^2+36 a+9$
$=9\left[4 a^2+4 a+1\right]$
$=9\left[(2 a)^2+2 \times 2 a x+(1)^2\right]$
$=9[2 a+1]^2$
View full question & answer→Question 722 Marks
Factorise: $p^2-10 p+25$
Answer$p^2-10 p+25$
$=(p)^2-2 \times p \times 5+(5)^2$
$=(p-5)^2$
$\{\because a^2- 2ab + b^2= (a - b)^2\}$
View full question & answer→Question 732 Marks
Factorise: $3(a-2 b)^2-5(a-2 b)$
Answer$3(a-2 b)^2-5(a-2 b)$
$ = (a - 2b)\{3(a - 2b) - 5\}$
$= (a - 2b)(3a - 6b - 5)$
View full question & answer→Question 742 Marks
$36c^2- (5a + b)^2$
Answer$= (6c)^2- (5a + b)^2$
$[\because a^2- b^2= (a + b)(a - b)\}$
$= (6c + 5a + b)(6c - 5a - b)$
View full question & answer→Question 752 Marks
Factorise: $12(2 x-3 y)^2-16(3 y-2 x)$
Answer$12(2 x-3 y)^2-16(3 y-2 x)$
$=12(2 x-3 y)^2+16(2 x-3 y)$
$ = 4(2x - 3y){3(2x - 3y) + 4} $
$= 4(2x - 3y)(6x - 9y + 4)$
View full question & answer→Question 762 Marks
Factorise:
$9a(3a - 5b) - 12a^2(3a - 5b)$
Answer$9a(3a - 5b) - 12a^2(3a - 5b) $
$= 3a(3a - 5b)(3 - 4a)$
View full question & answer→Question 772 Marks
Factorise:
$ x^2+14 x+49$
Answer$ x^2+14 x+49$
$=(x)^2+2 \times x \times 7+(7)^2 $
$ =(x+7)^2 $
View full question & answer→Question 782 Marks
Factorise:
$x^2+15 x+56$
Answer$x^2+15 x+56$
$=x^2+8 x+7 x+56$
${56 = 8 × 7, 15 = 8 + 7} $
$= x(x + 8) + 7(x + 8) $
$= (x + 8)(x + 7)$
View full question & answer→Question 792 Marks
Factorise: $\text{z}^2+\text{z}+\frac{1}{4}$
Answer$\text{z}^2+\text{z}+\frac{1}{4}$ $=(\text{z})^2+2\times\text{z}\times\frac{1}{2}+\Big(\frac{1}{2}\Big)^2$ $=\Big(\text{z}+\frac{1}{2}\Big)^2$
View full question & answer→Question 802 Marks
Factorise: $16 p^3-4 p$
Answer$16 p^3-4 p$
$=4 p\left[4 p^2-1\right]$
$=4 p(2 p)^2-(1)^2$
$=4 p(2 p+1)(2 p-1)$
View full question & answer→Question 812 Marks
Factorise: $y^2+7 y-144$
Answer$y^2+7 y-144$
$=y^2+16 y-9 y-144$
${144 = -16 × 9, 7 = 16 - 9}$
$= y(y + 16) - 9(y + 16) $
$= (y + 16)(y - 9)$
View full question & answer→Question 822 Marks
Factorise:
$16 a^2-144$
AnswerUsing: $a^2-b^2=(a+b)(a-b) $
$16 a^2-144=(4 a)^2=(12)^2$
$=(4 a+12)(4 a-12)$
$=4(a+3) \times 4(a-3)$
$=16(a+3)(a-3)$
View full question & answer→Question 832 Marks
Factorise: $3+23 z-8 z^2$
Answer$3+23 z-8 z^2$
$=3+24 z-z-8 z^2$
$\{3 × (-8) = -24, -24 = 24 × (-1), 23 = 24 - 1\}$
$= 3(1 + 8z) - z(1 + 8z)$
$ = (1 + 8z)(3 - z)$
View full question & answer→Question 842 Marks
Factorise:
$9 m^2+24 m+16$
Answer$9 m^2+24 m+16$
$=9(3 m)^2+2 \times 3 m \times 4+(4)^2] $
$ =(3 m+4)^2 $
$\{\therefore a2 + 2ab + b2 = (a + b)2\}$
View full question & answer→Question 852 Marks
Factorise:
$25 a^2-4 b^2+28 b c-49 c^2$
Answer$25 a^2-4 b^2+28 b c-49 c^2$
$=25-\left[4 b^2-28 b c+49 c^2\right]$
${\left[\because a^2-2 a b+b^2=(a-b)^2\right]}$
$=(5 a)^2-\left[(2 b)^2-2 \times 2 b \times 7 c+(7 c)^2\right] $
$ =(5 a)^2-(2 b-7 c)^2 $
$\left\{\because\left(a^2-b^2=(a+b)(a-b)\right\}\right.$
$ = (5a + 2b - 7c)(5a - 2b + 7c)$
View full question & answer→Question 862 Marks
Factorise: $ x^2-36 $
Answer$ x^2-36 $
$ =(x)^2-(6)^2\left\{\therefore a^2-b^2=(a+b)(a-b)\right\} $
$ =(x+6)(x-6) $
View full question & answer→Question 872 Marks
Factorise:
$x^2-4 x-12$
Answer$x^2-4 x-12$
$=x^2-6 x+2 x-12$
$\{-12 = -6 × 2, -4 = -6 + 2\}$
$= x(x - 6) + 2(x - 6) $
$= (x - 6)(x + 2)$
View full question & answer→Question 882 Marks
Factorise:
$ (a x+b y)^2+(b x-a y)^2$
Answer$ (a x+b y)^2+(b x-a y)^2$
$= (a^2 x^2+b^2 y^2+2 a x b y+b^2 x^2+a^2 y^2-2 b x a y$
$=a^2 x^2+b^2 y^2+b^2 x^2+a^2 y^2$
$=a^2 x^2+b^2 x^2+a^2 y^2+b^2 y^2$
$= x^2\left(a^2+b^2\right)+y^2\left(a^2+b^2\right)$
$=\left(a^2+b^2\right)\left(x^2+y^2\right) $
View full question & answer→Question 892 Marks
$x^2-y^2-2 y-1$
Answer$x^2-y^2-2 y-1$
$=x^2-\left(y^2+2 y+1\right)$
$=(x)^2-(y+1)^2$
$=(x+y+1)(x-y-1)$
View full question & answer→Question 902 Marks
Factorise:
$25-a^2-b^2-2 a b$
Answer$25-a^2-b^2-2 a b$
$=25-\left(a^2+b^2+2 a b\right)$
$=(5)^2-(a+b)^2$
$=(5+a+b)(5-a-b)$
View full question & answer→Question 912 Marks
Factorise:
$63 a^2 b^2-7$
Answer$63 a^2 b^2-7$
$=7\left(9 a^2 b^2-1\right)$
$=7(3 a b)^2-(1)^2$
$=7(3 a b+1)(3 a b-1)$
View full question & answer→Question 922 Marks
Factorise: $y^2-21 y+90$
Answer$y^2-21 y+90$
$=y^2-15 y-6 y+90$
$\{90 = (-15) × (-6), -21 = -15 - 6\}$
$= y(y - 15) - 6(y - 15) $
$= (y - 15)(y - 6)$
View full question & answer→Question 932 Marks
Factorise:
$z^2+12 x+27$
Answer$z^2+12 x+27$
$=z^2+9 z+3 z+27$
$\{27 = 9 × 3, 12 = 9 + 3\} $
$= z(z + 9) + 3(z + 9) $
$= (z + 9)(z + 3)$
View full question & answer→Question 942 Marks
Factorise: $100-(x-5)^2$
Answer$100-(x-5)^2$
$(10)^2-(x-5)^2$
$= (10 + x - 5)(10 - x + 5) $
$= (5 + x)(15 - x)$$
View full question & answer→Question 952 Marks
Factorise:
$x^2-11 x-42$
Answer$x^2-11 x-42$
$=x^2-14 x+3 x-42$
$\{-11 = -14 + 3, -42 = -14 × 3\}$
$= x(x - 14) + 3(x - 14)$
$= (x - 14)(x + 3)$
View full question & answer→Question 962 Marks
Factorise:
$x^3-3 x^2+x-3$
Answer$x^3-3 x^2+x-3$
$=x^2(x-3)+1(x-3)(x-3)$
$\left(x^2+1\right)$
View full question & answer→Question 972 Marks
Factorise:
$6 x^2-5 x-6$
Answer$6 x^2-5 x-6$
$=6 x^2-9 x+4 x-6$
$\{6 × (-6) = -36, -36 = -9 × 4, -5 = -9 + 4\}$
$= 3x(2x - 3) + 2(2x - 3)$
$ = (2x - 3)(3x + 2)$
View full question & answer→Question 982 Marks
Factorise:
$x^2+5 x-104$
Answer$x^2+5 x-104$
$=x^2+13 x-8 x-104$
$\{-104 = 13 × (-8), 5 = 13 - 8\}$
$= x(x + 13) - 8(x + 13) $
$= (x + 13)(x - 8)$
View full question & answer→Question 992 Marks
Factorise:
$3 x^5-48 x^3$
Answer$3 x^5-48 x^3$
$=3 x^3\left\{x^2-16\right\}$
$=3 x^3\left\{(x)^2-16\right\}$
$=3 x^3\left\{(x)^2-(4)^2\right\}$
$=3 x^3(x+4)(x-4)$
View full question & answer→Question 1002 Marks
Factorise:
$12 x^2-27$
Answer$12 x^2-27$
$=3\left(4 x^2-9\right)$
$=3(2 x)^2-(3)^2$
$=3(2 x+3)(2 x-3)$
View full question & answer→Question 1012 Marks
Factorise:
$6 x^2-17 x-3$
Answer$6 x^2-17 x-3$
$=6 x^2-18 x+x-3$
$\{6 × (-3) = -18, -18 = -18 × 1, -17 = -18 + 1\}$
$= 6x(x - 3) + 1(x - 3)$
$ = (x - 3)(6x + 1)$
View full question & answer→Question 1022 Marks
Factorise:
$x^2+5 x+6$
Answer$x^2+5 x+6$
$=x^2+2 x+3 x+6$
$\{6 = 2 × 3, 5 = 2 + 3\}$
$= x(x + 2) + 3(x + 2)$
$ = (x + 2)(x + 3)$
View full question & answer→Question 1032 Marks
Factorise:
$=16 a^2-225 b^2$
AnswerUsing: $a^2-b^2$
$=(a+b)(a-b)$
$=16 a^2-225 b^2$
$=(4 a)^2-(15 b)^2$
$=(4 a+15 b)(4 b-15 b)$
View full question & answer→Question 1042 Marks
Factorise:
$z^2+19 z-150$
Answer$z^2+19 z-150$
$=z^2+25 z-6 z-150$
$\{-150 = 25 × (-6), 19 = 25 - 6\}$
$= z(z + 25) - 6(z + 25)$
$ = (z + 25)(Z - 6)$
View full question & answer→Question 1052 Marks
Factorise:
$7 y^2-19 y-6$
Answer$7 y^2-19 y-6$
$=7 y^2-21 y+2 y-6$
$\{7 × (-6) = -42, -42 = -21 × 2, -19 = -21 + 3\}$
$= 7y(y - 3) + 2(y - 3) $
$= (y - 3)(7y + 2)$
View full question & answer→Question 1062 Marks
Factorise:
$x^2-9 x+20$
Answer$x^2-9 x+20$
$=x^2-5 x-4 x+20$
$\{20 = (-5) × (-4), -9 = -5 - 4\}$
$= x(x - 5) - 4(x - 5)$
$ = (x - 5)(x - 4)$
View full question & answer→Question 1072 Marks
Factorise:
$p^2+6 p+8$
Answer$p^2+6 p+8$
$=p^2+4 p+2 p+8$
$\{8 = 4 × 2, 6 = 4 + 2\}$
$ = p(p + 4) + 2(p + 4) $
$= (p + 4)(p + 2)$
View full question & answer→Question 1082 Marks
Factorise:
$121 a^2-88 a b+16 b^2$
Answer$121 a^2-88 a b+16 b^2$
$=(11 a)^2-2 \times 11 a \times 4 b+4(b)^2$
$=(11 a-4 b)^2$
View full question & answer→Question 1092 Marks
Factorise:
$2 x^2-17 x-30$
Answer$2 x^2-17 x-30$
$=2 x^2-20 x+3 x-30$
$\{2 × (-30) = -60, -17 = -20 + 3, -60 = -20 × 3\}$
$= 2x(x - 10) + 3(x - 10) $
$= (x - 10)(2x + 3)$
View full question & answer→Question 1102 Marks
Factorise:
$x^3-64$
Answer$x^3-64$
$=x\left(x^2-64\right)$
$=x(x)^2-(8)^2$
$=x(x+8)(x-8)$
View full question & answer→