Factorisation Using Algebraic Identities

Q.

Factorise the following expression: $a^2+8a+16$

Q.

Factorise the following expression: $25m^2+30m+9$.

Q.

Factorise:

$a^6-7a^3-8$

Q.

Factorise:

$4x^4-x^2-12x-36$

Q.

Factorise:

$8a^3-b^3-4ax+2bx$

Q. Question 5
Factorise:
(i) $x^3-2x^2-x+2$
(ii) $x^3-3x^2-9x-5$
(iii) $x^3+13x^2+32x+20$
(iv) $2y^3+y^2-2y-1$

Q. Factorize:
$6(2a+3b{)}^2-8(2a+3b)$

Q.

Prove that $\frac{0.85\times 0.85\times 0.85+0.15\times 0.15\times 0.15}{0.85\times 0.85-0.85\times 0.15+0.15\times 0.15}=1.$

Q.

Factorise:

$a(a-1)-b(b-1)$

Q.

Factorise:

$a^2-(2a+3b{)}^2$

Q.

Factorise:

$9a^2+3a-8b-64b^2$

Q.

The factors of $x^3-1+y^3+3xy$ are

1. $(x-1+y)(x^2+1+y^2+x+y-xy)$
   

2. $(x+y+1)(x^2+y^2+1-xy-x-y)$
   

3. $(x-1+y)(x^2-1-y^2+x+y+xy)$
   

4. $3(x+-1)(x^2+y^2-1)$
   

Q.

Factorise:

$4x^2+\frac{1}{4x^2}+1$

Q.

Factorise:

$a-b-a^3+b^3$

Q.

Factorise:

$a^3-27b^3+2a^{2}b-6a{b}^2$

Q.

Show that:

$\left(i\right){13}^3-5^3$ is divisible by 8.

$\left(ii\right){35}^3+{27}^3$ is divisible by 62.

Q.

Prove that $\frac{59\times 59\times 59-9\times 9\times 9}{59\times 59+59\times 9+9\times 9}=50.$

Q.

Factorise:

$4a^2-12a+9-49b^2$

Q.

Factorise:

$(a^2-1)(b^2-1)+4ab$

Q.

Factorised form of 23xy – 46x + 54y – 108 is

(a) (23x + 54) (y – 2)

(b) (23x + 54y) (y – 2)

(c) (23xy + 54y) (– 46x – 108)

(d) (23x + 54) (y + 2)

Q.

Question 32
Factorise the following:
(i) $1–64a^3–12a+48a^2$

(ii) $8p^3+\frac{12}{5}{p}^2+\frac{6}{25}p+\frac{1}{125}$

Q.

Question 36
Factorise:
(i) $a^3-8b^3-64c^3-24abc$

(ii) $2\sqrt{2}{a}^3+8b^3-27c^3+18\sqrt{2}abc$

Q.

Factorise:

$4a^2-49b^2+2a-7b$

Q.

Factorise: $4xy-x^2-4y^2+z^2$

Q.

Factorise:

$4a^2-(4b^2+4bc+c^2)$

Q.

Factorise:

$a^2+b^2-c^2-d^2+2ab-2cd$

Q.

Factorise:

$x^4+y^4-3x^2{y}^2$

Q.

Factorise:

$a^3-\frac{27}{a^3}$

Q.

Factorise:

$a^2-81(b-c{)}^2$

Q. Factorise:
$x^3+13x^2+32x+20$

1. $(x+1)(x+2)(x+10)$
2. $(x-1)(x+2)(x-10)$
3. $(x-1)(x-2)(x+10)$
4. $(x+1)(x-2)(x-10)$