Question 12 Marks
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
Answerar + br + at + bt = r(a + b)+ t(a + b)
= (a + b)(r + t)
View full question & answer→Question 72 Marks
Factorise:
$3 m^2+24 m+36$
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:
$x^2-x(a+2 b)+12 a b$
Answer$x ^2- x ( a +2 b)+2 ab$
$=x^2-x a-2 b x+2 a b$
$=x(x-a)-2 b x+2 a b$
$=x(x-a)-2 b(x-a)$
$=(x-a)(x-2 b)$
View full question & answer→Question 132 Marks
Factorise:
$x^2-5 x-24$
Answer$x^2-5 x-24$
$=x^2-8 x+3 x-24$
$\{-24=-8 \times 3,-5=-8+3\}$
$=x(x-8)+3(x-8)$
$=(x-8)(x+3)$
View full question & answer→Question 142 Marks
Factorise:
$49 a^2+84 a b+36 b^2$
Answer$49 a^2+84 a b+36 b^2$
$=(7 a)^2+2 \times 7 a \times 6 b+(6 b)^2$
$\left\{\because a^2+2 a b+b^2=(a+b)^2\right\}$
$=(7 a+6 b)^2$
View full question & answer→Question 152 Marks
Factorise:
$4 x^2-9 y^2$
Answer$4 x^2-9 y^2$
$=(2 x)^2-(3 y)^2$
$=(2 x+3 y)(2 x-3 y)$
$\left\{\because a^2-b^2=(a+b)(a-b)\right\}$
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
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$6 a b-b^2+12 a c-2 b c$
$=6 a b+12 a c-b^2-2 b c$
$=6 a(b+2 c)-b(b+2 c)$
$=(b+2 c)(6 a-b)$
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$x^2+x-132$
$=x^2+12 x-11 x-132$
$\{-132=12 \times(-11), 1=12-11\}$
$=x(x+12)-11(x+12)$
$ =(x+12)(x-11)$
View full question & answer→Question 292 Marks
Factorise:
$1-(b-c)^2$
Answer$1-(b-c)^2$
$=(1)^2-(b-c)^2$
$=(1+b+c)(1-b+c)$
$\left\{\because a^2-b^2=(a+b)(a-b)\right\}$
View full question & answer→Question 302 Marks
Factorise:
$9 a^2 b-25$
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:
$x^2-7 x-30$
Answer$x^2-7 x-30$
$=x^2-10 x+3 x-30$
$\{-30=-10 \times 3,-7=-10+3\}$
$=x(x-10)+3(x-10)$
$=(x-10)(x+3)$
View full question & answer→Question 322 Marks
Factorise:
$4 a^2-9$
Answer$4 a^2-9$
$=(2 a)^2-(3)^2$
$=(2 a+3)(2 a-3)\left\{\therefore a^2-b^2=(a+b)(a-b)\right\}$
View full question & answer→Question 332 Marks
Factorise:
$y^2+19 y+60$
Answer$y ^2+19 y +60$
$=y^2+19 y+60$
$\{60=15 \times 4,19=15+4\}$
$=y(y+15)+4(y+15)$
$=(x+15)(x+4)$
View full question & answer→Question 342 Marks
Factorise:
$63 a^2-112 b^2$
AnswerUsing: $a ^2- b ^2=( a + b )( a - b )$
$63 a^2-112 b^2$
$=7\left(9 a^2-16 b^2\right)$
$=7\left[(3 a)^2-(4 b)^2\right.$
$=7(3 a+4 b)(3 a-4 b)$
View full question & answer→Question 352 Marks
Factorise:
$1-6 x+9 x^2$
Answer$1-6 x+9 x^2$
$=(1)^2-2 \times 1 \times 3 x+(3 x)^2$
$=(1-3 x)^2$
$\{\because a 2-2 a b+b 2=(a-b) 2\}$
View full question & answer→Question 362 Marks
Factorise:
$q^2-10 q+21$
Answer$q^2-10 q+21$
$=q^2+7 q-3 q+21$
$\{21=(-7) \times(-3),-10=-7-3\}$
$=q(q-7)-3(q-7)$
$=(q-7)(q-3)$
View full question & answer→Question 372 Marks
Factorise:
$6 p^2+11 p-10$
Answer$6 p^2+11 p-10$
$=6 x^2+15 x-4 x-10$
$\{6 \times(-10)=60,-60=15 \times(-4), 11=15-4\}$
$=3 x(2 x+5)-2(2 x+5)$
$=(3 x-2)(2 x+5)$
View full question & answer→Question 382 Marks
Factorise:
$3 x^2+10 x+8$
Answer$3 x^2+10 x+8$
$=3 x^2+6 x+4 x+8$
$\{24=3 \times 8,24=6 \times 4,10=6+4\}$
$=3 x(x+2)+4(x+2)$
$=(x+2)(3 x+4)$
View full question & answer→Question 392 Marks
Factorise:
$28-31 x-5 x^2$
Answer$28-31 x-5 x^2$
$=28-35 x+4 x-5 x^2$
$\{28 \times(-5)=-140,-140=-35 \times 4,-31=-35+4\}$
$=7(4-5 x)+x(4-5 x)$
$=(4-5 x)(7+x)$
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$y ^2+10 y +24$
$=y^2+6 y+4 y+24$
$\{24=6 \times 4,10=6+4\}$
$=y(y+6)+4(y+6)$
$=(y+6)(y+4)$
View full question & answer→Question 432 Marks
Factorise:
$m^2+2 m^2 n^2+n^4$
Answer$m^2+2 m^2 n^2+n^4$
$=\left(m^2\right)^2+2 m^2 n^2+\left(n^2\right)^2$
$=\left(m^2+n^2\right)^2$
$\left\{\because a^2+2 a b+b^2=(a+b)^2\right\}$
View full question & answer→Question 442 Marks
Factorise:
$2 x^2+x-45$
Answer$2 x^2+x-45$
$=2 x^2+10 x-9 x-45$
$\{2 \times(-45)=-90,-90=(10) \times(-9), 1=10-9\}$
$=2 x(x-5)+9(x-5)$
$=(x-5)(2 x+9)$
View full question & answer→Question 452 Marks
Factorise:
$9 a^2-b^2+4 b-4$
Answer$9 a^2-b^2+4 b-4$
$=9 a^2-\left(b^2-4 b+4\right)$
$=(3 a)^2-\left[(b)^2-2 \times b \times 2+(2)^2\right.$
$=(3 a)^2-(b-2)^2$
$\left\{\because a^2-2 a b+b^2=(a-b)^2\right\}$
$=(3 a+b-2)(3 a-b+2)$
$\left\{\because a^2-b^2=(a+b)(a-b)\right\}$
View full question & answer→Question 462 Marks
Factorise:
$7 x^2-19 x-6$
Answer$7 x^2-19 x-6$
$=7 x^2-21 x+2 x-6$
$\{7 \times(-6)=-42,-42=-21 \times 2,-19=-21+2\}$
$=7 x(x-3)+2(x-3)$
$=(x-3)(7 x+2)$
View full question & answer→Question 472 Marks
Factorise:
$p^2-4 p-11$
Answer$p^2-4 p-11$
$=p^2+11 p-7 p-77$
$\{-77=-11 \times 7,-4=-11+7\}$
$=p(p-11)+7(p-11)$
$=(p-11)(p+7)$
View full question & answer→Question 482 Marks
Factorise:
$(1+3)^2-(1-m)^2$
Answer$(1+3)^2-(1-m)^2$
$=(1+m+1-m)(1+m-1+m)$
$\{\because a 2-b 2=(a+b)(a-b)\}$
$= 2l × 2m = 4lm$
View full question & answer→Question 492 Marks
Factorise:
$x^2-10 x+24$
Answer$x^2-10 x+24$
$=x^2-6 x-4 x+24$
$\{24=(-6) \times(-4),-10=-6-4\}$
$=x(x-6)-4(x-6)$
$=(x-6)(x-4)$
View full question & answer→Question 502 Marks
Factorise:
$81-49 x^2$
Answer$81-49 x^2$
$=(9)^2-(7 x)^2$
$=(9+7 x)(9-7 x)\left\{\because a^2-b^2=(a+b)(a-b)\right\}$
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:
$a b^2+(a-1) b-1$
Answer$=a b^2+a b-b-1$
$=a b(b+1)-1(b+1)$
$=(b+1)(a b-1)$
View full question & answer→Question 532 Marks
Evalute:
$\left\{(7.8)^2-(2.2)^2\right\}$
Answer$(7.8)^2-(2.2)^2$
$=(7.8+2.2)(7.8-2.2)$
$=10.00 \times 5.6$
$=56$
View full question & answer→Question 542 Marks
Factorise:
$x^2-x z+x y-y z$
View full question & answer→Question 552 Marks
Factorise:
$a^2+6 a-91$
Answer$a^2+6 a-91$
$=a^2+13 a-7 a-91$
$\{-91=13 \times(-7), 6=13-7\}$
$=a(a+13)-7(a+13)$
$=(a+13)(a-7)$
View full question & answer→Question 562 Marks
Factorise:
$x^2+13 x+40$
Answer$x^2+13 x+40$
$=x^2+5 x+8 x+40$
$\{40=5 \times 8,13=5+8\}$
$=x(x+5)+8(y+5)$
$=(x+5)(x+8)$
View full question & answer→Question 572 Marks
Factorise:
$x^2-22 x+117$
Answer$x^2-22 x+117$
$=x^2-13 x-9 x+117$
$\{117=(-13) \times(-9),-22=-13-9\}$
$=x(x-13)-9(y-13)$
$=(x-9)(x-13)$
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$4 n^2-8 n+3$
$=4 n^2-6 n-2 n+3$
$\{4 \times 3=12,12=(-6) \times(-2),-8=-6-2\}$
$=2 n(2 n-3)-1(2 n-3)$
$=(2 n-3)(2 n-1)$
View full question & answer→Question 602 Marks
Factorise:
$(I+m)^2-41 m$
Answer$(I+m)^2-41 m$
$=I^2+m^2+2 I m-4 I m$
$=I^2+m^2-2 I m$
$=I^2-2 I m+m^2$
$=(I-m)^2$
$\left\{\because a^2+2 a b+b^2=(a+b)^2\right\}$
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$z^2-12 z-45$
$=z^2-15 z+3 z-45$
$\{-45=-15 \times 3,-12=-15+3\}$
$=z(z-15)+3(z-15)$
$=(z-15)(z+3)$
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$y^2-6 y-135$
$=y^2-15+9 y-135$
$\{-135=-15 \times 9,-6=-15+9\}$
$=y(y-15)+9(y-15)$
$=(y-15)(y+9)$
View full question & answer→Question 652 Marks
Factorise:
$3 z^2-10 z+8$
Answer$3 z^2-10 z+8$
$=3 z^2-6 z-4 z+8$
$\{24=3 \times 8,24=(-6) \times(-4),-10=-6-4\}$
$=3 z(z-2)-4(z-2)$
$=(z-2)(3 z-4)$
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$3 y^2+14 y+8$
$=3 y^2+12 y+2 y+8$
$\{24=3 \times 8,24=12 \times 2,14=12+2\}$
$=3 y(y+4)+2(y+4)$
$=(y+4)(3 y+2)$
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:
$x^2-a x-b x+a b$
Answer$x 2-a x-b x+a b$
$=x(x-a)-b(x-a)$
$=(x-a)(x-b)$
View full question & answer→Question 712 Marks
Factorise $: 36a^2 + 36a + 9$
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 \times 1+(1)^2\right]$
$ = 9[2 a+1]^2$
View full question & answer→Question 722 Marks
Factorise:
$p^2-10 p+25$
Answer$p^2-10 p+25$
$=(p)^2-2 \times p \times 5+(5)^2$
$=(p-5)^2$
$\left\{\because a^2-2 a b+b^2=(a-b)^2\right\}$
View full question & answer→Question 732 Marks
Factorise:
$3(a-2 b)^2-5(a-2 b)$
Answer$3(a-2 b)^2-5(a-2 b)$
$=(a-2 b)\{3(a-2 b)-5\}$
$=(a-2 b)(3 a-6 b-5)$
View full question & answer→Question 742 Marks
$36 c^2-(5 a+b)^2$
Answer$(6 c)^2-(5 a+b)^2$
${\left[\because a^2-b^2=(a+b)(a-b)\right\}}$
$=(6 c+5 a+b)(6 c-5 a-b)$
View full question & answer→Question 752 Marks
Factorise:
$12(2 x-3 y)^2-16(3 y-2 x)$
Answer$12(2 x-3 y)^2-16(3 y-2 x)$
$=12(2 x-3 y)^2+16(2 x-3 y)$
$=4(2 x-3 y)\{3(2 x-3 y)+4\}$
$=4(2 x-3 y)(6 x-9 y+4)$
View full question & answer→Question 762 Marks
Factorise:
$9 a(3 a-5 b)-12 a^2(3 a-5 b)$
Answer$9 a(3 a-5 b)-12 a^2(3 a-5 b)$
$=3 a(3 a-5 b)(3-4 a)$
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$x^2+15 x+56$
$=x^2+8 x+7 x+56$
$\{56=8 \times 7,15=8+7\}$
$=x(x+8)+7(x+8)$
$=(x+8)(x+7)$
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$y ^2+7 y -144$
$=y^2+16 y-9 y-144$
$\{144=-16 \times 9,7=16-9\}$
$=y(y+16)-9(y+16)$
$=(y+16)(y-9)$
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$3+23 z-8 z^2$
$=3+24 z-z-8 z^2$
$\{3 \times(-8)=-24,-24=24 \times(-1), 23=24-1\}$
$=3(1+8 z)-z(1+8 z)$
$=(1+8 z)(3-z)$
View full question & answer→Question 842 Marks
Factorise:
$9 m^2+24 m+16$
Answer$9 m^2+24 m+16$
$\left.=9(3 m)^2+2 \times 3 m \times 4+(4)^2\right]$
$=(3 m+4)^2$
$\{\therefore a 2+2 a b+b 2=(a+b) 2\}$
View full question & answer→Question 852 Marks
Factorise:
$25 a^2-4 b^2+28 b c-49 c^2$
Answer$25 a^2-4 b^2+28 b c-49 c^2$
$=25-\left[4 b^2-28 b c+49 c^2\right]$
${\left[\because a^2-2 a b+b^2=(a-b)^2\right]}$
$=(5 a)^2-\left[(2 b)^2-2 \times 2 b \times 7 c+(7 c)^2\right]$
$=(5 a)^2-(2 b-7 c)^2$
$\left\{\because\left(a^2-b^2=(a+b)(a-b)\right\}\right.$
$=(5 a+2 b-7 c)(5 a-2 b+7 c)$
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$x^2-4 x-12$
$=x^2-6 x+2 x-12$
$\{-12=-6 \times 2,-4=-6+2\}$
$=x(x-6)+2(x-6)$
$=(x-6)(x+2)$
View full question & answer→Question 882 Marks
Factorise:
$(a x+b y)^2+(b x-a y)^2$
Answer$(a x+b y)^2+(b x-a y)^2$
$=\left(a^2 x^2+b^2 y^2+2 a x b y+b^2 x^2+a^2 y^2-2 b x a y\right.$
$=a^2 x^2+b^2 y^2+b^2 x^2+a^2 y^2$
$=a^2 x^2+b^2 x^2+a^2 y^2+b^2 y^2$
$=x^2\left(a^2+b^2\right)+y^2\left(a^2+b^2\right)$
$=\left(a^2+b^2\right)\left(x^2+y^2\right)$
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$y^2-21 y+90$
$=y^2-15 y-6 y+90$
$\{90=(-15) \times(-6),-21=-15-6\}$
$=y(y-15)-6(y-15)$
$=(y-15)(y-6)$
View full question & answer→Question 932 Marks
Factorise:
$z^2+12 x+27$
Answer$z^2+12 x+27$
$=z^2+9 z+3 z+27$
$\{27=9 \times 3,12=9+3\}$
$=z(z+9)+3(z+9)$
$=(z+9)(z+3)$
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$x^2-11 x-42$
$=x^2-14 x+3 x-42$
$\{-11=-14+3,-42=-14 \times 3\}$
$=x(x-14)+3(x-14)$
$=(x-14)(x+3)$
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$6 x^2-5 x-6$
$=6 x^2-9 x+4 x-6$
$\{6 \times(-6)=-36,-36=-9 \times 4,-5=-9+4\}$
$=3 x(2 x-3)+2(2 x-3)$
$=(2 x-3)(3 x+2)$
View full question & answer→Question 982 Marks
Factorise:
$x^2+5 x-104$
Answer$x^2+5 x-104$
$=x^2+13 x-8 x-104$
$\{-104=13 \times(-8), 5=13-8\}$
$=x(x+13)-8(x+13)$
$=(x+13)(x-8)$
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$6 x^2-17 x-3$
$=6 x^2-18 x+x-3$
$\{6 \times(-3)=-18,-18=-18 \times 1,-17=-18+1\}$
$=6 x(x-3)+1(x-3)$
$=(x-3)(6 x+1)$
View full question & answer→Question 1022 Marks
Factorise:
$x^2+5 x+6$
Answer$ x^2+5 x+6$
$=x^2+2 x+3 x+6$
$\{6=2 \times 3,5=2+3\}$
$=x(x+2)+3(x+2)$
$=(x+2)(x+3)$
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$z^2+19 z-150$
$=z^2+25 z-6 z-150$
$\{-150=25 \times(-6), 19=25-6\}$
$=z(z+25)-6(z+25)$
$=(z+25)(z-6)$
View full question & answer→Question 1052 Marks
Factorise:
$7 y^2-19 y-6$
Answer$7 y^2-19 y-6$
$=7 y^2-21 y+2 y-6$
$\{7 \times(-6)=-42,-42=-21 \times 2,-19=-21+3\}$
$=7 y(y-3)+2(y-3)$
$=(y-3)(7 y+2)$
View full question & answer→Question 1062 Marks
Factorise:
$x^2-9 x+20$
Answer$x^2-9 x+20$
$=x^2-5 x-4 x+20$
$\{20=(-5) \times(-4),-9=-5-4\}$
$=x(x-5)-4(x-5)$
$=(x-5)(x-4)$
View full question & answer→Question 1072 Marks
Factorise:
$p^2+6 p+8$
Answer$p^2+6 p+8$
$=p^2+4 p+2 p+8$
$\{8=4 \times 2,6=4+2\}$
$=p(p+4)+2(p+4)$
$=(p+4)(p+2)$
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$2 x^2-17 x-30$
$=2 x^2-20 x+3 x-30$
$\{2 \times(-30)=-60,-17=-20+3,-60=-20 \times 3\}$
$=2 x(x-10)+3(x-10)$
$=(x-10)(2 x+3)$
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→