Question 12 Marks
factorise: $5 x^2-\frac{20 x^4}{9}$
Answer$ 5 x^2-\frac{20 x^4}{9}$
$ =5 x^2\left[1-\frac{4 x^2}{9}\right]$
$ =5 x^2\left[1-\frac{2 x}{3}\right]\left[1+\frac{2 x}{3}\right]$
View full question & answer→Question 22 Marks
factorise: $x^2 - 2xy + y^2 - z^2$
Answer$x^2 - 2xy + y^2 - z^2$
$= (x^2 - 2xy + y^2) - z^2$
$= (x - y)^2 - (z)^2$
$= (x - y - z)(x - y + z)$
View full question & answer→Question 32 Marks
factorise: $(2x - y)^3 - (2x - Y)$
Answer$(2x - y)^3 - (2x - Y)$
$= (2x - y)[(2x - y)^2 - 1]$
$= (2x - y)(2x - y - 1) (2x - y + 1)$
View full question & answer→Question 42 Marks
factorise: $64a^2b - 144b^3$
Answer$64a^2b - 144b^3$
$= 16b (4a^2 - 9b^2)$
$= 16b [(2a)^2 - (3b)^2]$
$= 16b (2a + 3b)(2a - 3b)$
View full question & answer→Question 52 Marks
factorise: $54a^2b^2 - 6$
Answer$54a^2b^2 - 6$
$= 6(9a^2b^2 - 1) = 6[(3ab)^2 - (1)^2]$
$= 6 (3ab - 1)(3ab + 1)$
View full question & answer→Question 62 Marks
factorise: $2a^3 - 50a$
Answer$2a^3 - 50a$
$= 2a (a^2 - 25) = 2a(a^2 - 5^2)$
$= 2a (a - 5) (a + 5)$
View full question & answer→Question 72 Marks
factorise: $3a^2x - bx + 3a^2 - b$
Answer$3a^2x - bx + 3a^2 - b$
$= x(3a^2 - b) + 1 (3a^2 - b)$
$= (x + 1)(3a^2 - b)$
View full question & answer→Question 82 Marks
factorise: $x^2y^2 - 3xy - 40$
Answer$x^2y^2 - 3xy - 40$
$= x^2y^2 - 8xy + 5xy - 40$
$= xy (xy - 8) + 5 (xy - 8)$
$= (xy - 8)(xy + 5)$
View full question & answer→Question 92 Marks
Factorise: $9 x^2-\frac{1}{16}$
Answer$ 9 x^2-\frac{1}{16}$
$ =(3 x)^2-\left(\frac{1}{4}\right)^2$
$ =\left(3 x+\frac{1}{4}\right)\left(3 x-\frac{1}{4}\right)$
View full question & answer→Question 102 Marks
factorise : $a^2 - (b - c)^2$
Answer$a^2 - (b - c)^2$
$= (a - (b - c)) (a + b - c) ...[a^2 - b^2 = (a - b)(a + b)]$
$= (a - b + c) (a + b - c)$
View full question & answer→Question 112 Marks
factorise : $xy^2 + (x - 1) y - 1$
Answer$xy^2 + (x - 1) y - 1$
$= xy^2+ xy - y - 1= xy (y + 1) - 1 (y + 1)$
$= (xy - 1)(y + 1)$
View full question & answer→Question 122 Marks
Factorise : $a^2 - ab(1 - b) - b^3$
Answer$a^2 - ab(1 - b) - b^3$
$= a^2 - ab + ab^2 - b^3$
$= a(a - b) + b^2(a - b)$
$= (a - b) (a + b^2)$
View full question & answer→Question 132 Marks
factorise : $9a (x-2y)^4 - 12a (x - 2y)^3$
Answer$9a (x-2y)^4 - 12a (x - 2y)^3$
$= 3a (x - 2y)^3 [3(x - 2y) - 4]$
$=3a(x - 2y)^3 [3x -6y - 4]$
View full question & answer→Question 142 Marks
factorise : $8(2a + 3b)^3 - 12(2a + 3b)^2$
Answer$8(2a + 3b)^3 - 12(2a + 3b)^2$
$= 4 (2a + 3b)^2 [2 (2a + 3b) - 3]$
$= 4 (2a + 3b)^2 [4a + 6b - 3]$
View full question & answer→Question 152 Marks
Factorise completely: $ x^2 - y^2 - 3x - 3y$
Answer$x^2 - y^2 - 3x - 3y$
$= (x^2 - y^2) - 3 (x + y)$
$= (x + y) (x - y) - 3(x + y)$
$= (x + y)(x - y -3)$
View full question & answer→Question 162 Marks
Factorise completely: $a^4 - b^4$
Answer$a^4 - b^4$
$= (a2)2 - (b2)2$
$= (a^2 + b^2) (a^2 - b^2)$
$= (a^2 + b^2)(a + b)(a - b)$
View full question & answer→Question 172 Marks
Factorise completely: $25x^3 - x$
Answer$25x^3 - x$
$= x (25x^2 - 1)$
$= x [(5x)^2 - (1)^2]$
$= x (5x + 1)(5x - 1)$
View full question & answer→Question 182 Marks
Factorise completely: $8x^2y - 18y^3$
Answer$8x^2y - 18y^3$
$= 2y (4x^2 - 9y^2)$
$= 2y[(2x)^2 - (3y)^2]$
$= 2y (2x + 3y) (2x - 3y)$
View full question & answer→Question 192 Marks
Factorise completely: $2 - 8x^2$
Answer$2 - 8x^2 = 2(1 - 4x^2)$
$= 2[(1)^2 - (2x)^2]$
$= 2(1 + 2x) (1 - 2x)$
Note: $a^2 - b^2 = (a+b) (a-b)$
View full question & answer→Question 202 Marks
Factorise completely : $2a^2b^2 - 98b^4$
Answer$2a^2b^2 - 98b^4$
$= 2b^2 (a^2 - 49b^2)= 2b^2 [(a)^2 - (7b)^2]$
$= 2b^2 (a + 7b)(a - 7b)$
View full question & answer→Question 212 Marks
Factorise completely : $a^2 + 2ab + b^2 - c^2$
Answer$a^2 + 2ab + b^2 - c^2$
$= (a^2 + 2ab + b^2) - c^2$
$= (a + b)2 - (c)^2$
$= (a + b+ c) (a + b - c)$
View full question & answer→Question 222 Marks
In the case find whether the trinomial is a perfect square or not : $x^2 - 4x + 16$
Answer$x^2 - 4x + 16$
$= (x)^2 - x \times 4 + (4)^2$
$= a - ab + b^2$
$\therefore[$Taking $x = a,$ and $4 = b]$
$\therefore$ The given trinomial cannot be expressed as $a^2 - 2ab + b^2$.
Hence, it is not a perfect square $z$
View full question & answer→Question 232 Marks
In the case find whether the trinomial is a perfect square or not: $9b^2 + 12b + 16$
Answer$9b^2 + 12b + 16$
$= (3b)^2 + 3b \times 4 + (4)^2$
$= x^2 + xy + y^2 ... [$Taking $3b = x$, and $4 = y]$
$\therefore $The given trinomial cannot be expressed as $x^2 + 2xy + y^2$ .
Hence, it is not a perfect square.
View full question & answer→Question 242 Marks
In the case find whether the trinomial is a perfect square or not: $4x^2 + 4x + 1$
Answer$4x^2 + 4x + 1$
$= (2x)^2 + 2 \times 2x \times 1 + (1)^2$
$=(2x + 1)^2 [\because a^2 - 2ab + b^2 = (a - b)^2]$
$\therefore$ The given trinomial $4x^2 + 4x + 1$ is a perfect square.
View full question & answer→Question 252 Marks
In the case find whether the trinomial is a perfect square or not: $a^2 - 10a + 25$
Answer$a^2 - 10a + 25$
$= (a)^2 - 2 \times a \times 5 + (5)^2$
$= (a - 5)^2 [\because a^2 - 2ab + b^2 = (a - b)^2]$
$\therefore$ The given trinomial $a^2 - 10a + 25$ is a perfect square.
View full question & answer→Question 262 Marks
In the case find whether the trinomial is a perfect square or not: $x^2 + 14x + 49$
Answer$x^2 + 14x + 49$
$= (x)^2 + 2 \times x \times 7 + (7)^2$
$= (x + 7)^2 ...[a^2 + 2ab + b^2=(a + b)^2]$
$\therefore$ The given trinomial $x^2 + 14x + 49$ is a perfect square.
View full question & answer→Question 272 Marks
Factorise completely: $x^2 - y^2 - 2x + 2y$
Answer$x^2 - y^2 - 2x + 2y$
$= (x^2 - y^2) - 2(x - y)= (x + y) (x - y) - 2(x - y)$
$= (x - y)(x + y - 2)$
View full question & answer→Question 282 Marks
factorise: $a^2 - 5a+ 6$
Answer$a^2 - 5a+ 6$
$= a^2 - 3a - 2a + 6$
$= a(a - 3) - 2(a - 3)$
$= (a - 3)(a - 2)$
View full question & answer→Question 292 Marks
factorise: $a^2 + 5a + 6$
Answer$a^2 + 5a + 6$
$= a^2 + 2a + 3a + 6$
$= a(a + 2) + 3(a + 2)$
$= (a + 2) (a + 3)$
View full question & answer→Question 302 Marks
factorise: $x^2 + 4x + 3$
Answer$x^2 + 4x + 3$
$= x^2 + 3x + x + 3$
$= x(x + 3) + 1 (x + 3)$
$= (x + 3) (x + 1)$
View full question & answer→Question 312 Marks
factorise: $x^2 + 6x + 8$
Answer$x^2 + 6x + 8$
$= x^2 + 4x + 2x + 8$
$= x(x + 4) + 2(x + 4)$
$= (x+4) (x+2)$
View full question & answer→Question 322 Marks
factorise: $2a^2 + 7a + 6$
Answer$2a^2 + 7a + 6$
$= 2a^2 + 4a + 3a + 6$
$= 2a(a + 2) + 3(a + 2)$
$= (a + 2)(2a + 3)$
View full question & answer→Question 332 Marks
Factorise: $(5a - 2b)^2 - (2a - b)^2$
Answer$(5a - 2b)^2 - (2a - b)^2$
$= (5a - 2b + 2a - b) (5a - 2b - 2a + b)$
$= (7a - 3b) (3a - b)$
View full question & answer→Question 342 Marks
Factorise: $\frac{4}{25}-25 b^2$
Answer$ \frac{4}{25}-25 b^2$
$ =\left(\frac{2}{5}\right)^2-(5 b)^2$
$ =\left(\frac{2}{5}+5 b\right)\left(\frac{2}{5}-5 b\right) \ldots\left[\mathrm{a}^2-\mathrm{b}^2=(\mathrm{a}+\mathrm{b})(\mathrm{a}-\mathrm{b})\right]$
View full question & answer→Question 352 Marks
Factorise: $4x^2 - 81y^2$
Answer$4x^2 - 81y^2$
$= (2x)^2 – (9y)^2$
$= (2x + 9y) (2x – 9y) ...[a^2 – b^2 = (a + b) (a – b)]$
View full question & answer→Question 362 Marks
Factorise: $1 - 100a^2$
Answer$1 - 100a^2$
$= (1)^2 – (10a)^2$
$= (1 + 10a) (1 – 10a) ...[a^2 – b^2 = (a + b) (a – b)]$
View full question & answer→Question 372 Marks
Factorise: $16 - 9x^2$
Answer$16 – 9x^2$
$= (4)^2 – (3x)^2$
$= (4 + 3x) (4 – 3x) ...[a^2 – b^2 = (a + b) (a – b)]$
View full question & answer→Question 382 Marks
Factorise: $(4.5)^2 – (1.5)^2$
Answer$(4.5)^2 – (1.5)^{2}$
$= (4.5 + 1.5) (4.5 - 1.5) ...[a^2 – b^2 = (a + b) (a – b)]$
$= 6 \times 3 = 18$
View full question & answer→Question 392 Marks
Factorise: $(0·7)^2 - (0·3)^2$
Answer$(0·7)^2 - (0·3)^2$
$= (0.7 + 0.3) (0.7 - 0.3) ....[a^2 – b^2 = (a + b) (a – b)]$
$= 1 \times 0.4 = 0.4$
View full question & answer→Question 402 Marks
Factorise : $3x^5 - 6x^4 - 2x^3 + 4x^2 + x - 2$
Answer$3x^5 - 6x^4 - 2x^3 + 4x^2 + x - 2$
$= 3x^4 (x - 2) - 2x^2 (x - 2) + 1 (x - 2)$
$= (x - 2) (3x^4 - 2x^2 + 1)$
View full question & answer→Question 412 Marks
Factorise : $xy - ay - ax + a^2 + bx - ab$
Answer$xy - ay - ax + a^2 + bx - ab$
$= y (x - a) - a (x - a) + b (x - a)$
$= (x - a) (y - a + b)$
View full question & answer→Question 422 Marks
Factorise : $2a - 4b - xa + 2bx$
Answer$2a - 4b - xa + 2bx$
$= 2 (a - 2b) - x (a - 2b)$
$= (a - 2b) (2 - x)$
View full question & answer→Question 432 Marks
Factorise : $a^3 -a^2 +a -1$
Answer$a^3 -a^2 +a -1$
$= a^2 (a - 1) + 1 (a - 1)$
$= (a - 1) (a^2 + 1)$
View full question & answer→Question 442 Marks
Factorise : $ab - 2b + a^2 - 2a$
Answer$ab - 2b + a^2 - 2a$
$= b(a - 2) + a(a - 2)$
$= (a - 2) (b + a)$
View full question & answer→Question 452 Marks
Factorise : $2ab^2c - 2a + 3b^3c - 3b - 4b^2c^2 + 4c$
Answer$2ab^2c - 2a + 3b^3c - 3b - 4b^2c^2 + 4c$
$= 2a (b^2c - 1) + 3b (b^2c - 1) - 4c (b^2c - 1)$
$= (b^2c - 1) (2a + 3b - 4c)$
View full question & answer→Question 462 Marks
Factorise : $a^2 + ax + ab + bx$
Answer$a^2 + ax + ab + bx$
$=(a2 + ax) + (ab + bx)$
$= a(a + x) + b (a + x)$
$= (a + x) (a + b)$
View full question & answer→Question 472 Marks
Factorise : $ax + 2bx + 3cx - 3a - 6b - 9c$
Answer$ax + 2bx + 3cx - 3a - 6b - 9c$
$= x (a + 2b + 3c) - 3 (a + 2b + 3c)$
$= (a + 2b + 3c) (x - 3)$
View full question & answer→Question 482 Marks
Factorise : $2ab^2 - aby + 2cby - cy^2$
Answer$2ab^2 - aby + 2cby - cy^2$
$= 2b (ab + cy) - y (ab + cy)$
$= (ab + cy) (2b - y)$
View full question & answer→Question 492 Marks
Factorise : $ab^2 - (a - c) b - c$
Answer$ab^2 - (a - c) b - c$
$= ab^2 - ab + bc - c$
$= ab (b - 1) + c (b - 1)$
$= (b - 1) (ab + c)$
View full question & answer→Question 502 Marks
Factorise : $a(b - c) - d(c - b)$
Answer$a(b - c) - d(c - b)$
$= a (b - c) + d (b - c)$
$= (b - c) (a + d)$
View full question & answer→