Factorization of Expressions Reducible to Difference of Two Squares

Q.

Factorise:

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

Q. Factorise $a^3-27$.

1. $=(a-3)(a^2+5a+9)$
2. $=(a+3)(a^2+5a+9)$
3. $(a-3)(a^2-5a+9)$
4. $(a-3)(a^3+5a+9)$

Q. Factorise $98(a+b{)}^2-2$

1. $2[7a+7b+1][7a+b-1]$
2. $2[7a+7b+1][7a+b+1]$
3. $2[7a+7b-1][7a+b-1]$
4. $2[7a-7b+1][7a+b-1]$

Q.

Factorize: $75(a+b{)}^2-48(a-b{)}^2$.

1. $3(a+9b)(9a+b))$

2. $3(a+3b)(3a+b))$

3. $3(a-9b)(9a+b))$

4. $3(a-9b)(9a-b))$

Q. Factorise: $a^2+b^2-c^2-d^2+2ab-2cd$

1. $(a+b-c-d)(a+b+c+d)$
2. $(a+b+c+d{)}^2$
3. $(a-b-c+d)(a-b+c+d)$
4. $(a+b-c+d)(a+b+c+d)$

Q. How do you factor $x^2-25$?

Q. Factorize: $24a^3+37a^2-5a$

1. $(a+1)(8a-1)(3a+5)$
2. $a(8a-1)(3a+5)$
3. $a(8a+1)(3a-5)$
4. $(8a-1)(3a+5)$

Q. Factorise: $27x^3+y^3+z^3-9xyz$

Q. The expression $(2x^2-7x-15)$ is factorizable.

1. True
2. False

Q. Factorize
$25x^2+16y^2+4z^2-40xy+16yz-20xz$

Q.

How do you factorize $a^2-2ab+b^2$?

Q. Factorise: $(a^2+b^2-4c^2{)}^2-4a^2{b}^2$

1. $(a^2+b^2+4c^2-2ab)(a^2+b^2+4c^2+2ab)$
2. $(a^2+b^2-4c^2-2ab{)}^2$
3. $(a^2+b^2-4c^2-2ab)(a^2+b^2-4c^2+2ab)$
4. $(a^2-b^2-4c^2-2ab)(a^2-b^2-4c^2+2ab)$

Q. Factorise $4x^2-12ax-y^2-z^2-2yz+9a^2$

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

Q. Factorise $4xy-x^2-4y^2+z^2$

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

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

1. $=(2a-b)[4a^2+b^2+2ab-2x]$
   
2. $(2a-b)[4a^2+b+ab-2x]$
3. $(2a-b)[4a^2-b^2-2ab+2x]$
   
4. $(2a-b)[4a^2+b-2ab+2x]$
   

Q. Simplify the square root of the polynomial using factorisation method: $\frac{a^2}{a^2-b^2}+\frac{b^2}{b^2-a^2}$

1. $\sqrt{1}$
2. $-1$
3. $1$
4. $\sqrt{-1}$

Q. Factorise $a^6-b^6$

1. $(a+b)(a-b)(a^2+b^2+a^2{b}^2)$
2. $(a-b)(a-b)(a^4+b^2+a^2{b}^2)$
3. $=(a+b)(a-b)(a^4+b^4+a^2{b}^2)$
4. $(a+b)(a-b)(a^4+b^4+ab)$

Q. Factors of $(x^2-2xy+y^2)-z^2$ are

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

Q. Factorise $27a^3+8b^3-18a^{2}b-12a{b}^2$

Q. Factorise: $a^{12}-b^{12}$

1. $(a^6+b^6)(a+b)(a^2-ab-b^2)(a^2+ab+b^2)$
2. $(a^6-b^6)(a+b)(a^2-ab+b^2)(a^2+ab+b^2)$
3. $(a^2+b^2)(a^4+b^4-a^2{b}^2)(a+b)(a^2+b^2-ab)(a-b)(a^2+b^2+ab)$
4. $(a^6+b^6)(a-b)(a^2-ab+b^2)(a^2+ab+b^2)$

Q.

Write the factorisation of

$4a^{2}b$

Q. The factorisation of $a^4-1$ is equal to .

1. $(a+1)(a-1)(a^2+1)$
2. $(a-1)(a-1)(a^2+1)$
3. $(a+1)(a+1)(a^2+1)$
4. $(a+1)(a-1)(a^2-1)$

Q. Factorise $32a^4-8a^4$

1. $8a^2(2a-1)(2a+1)$
2. $8a(2a-1)(2a+1)$
3. $4a^2(2a-1)(2a+1)$
4. $32a^2(2a+1)$

Q. $a^3+b^3=(a+b)(a^2+ab+b^2)$

1. False
2. True

Q. Factorise: $a^2(b+c)-(b+c{)}^3$

1. $(b+c)\left[\right(a-b-c\left)\right(a+b+c\left)\right]$
2. $(b-c)\left[\right(a-b-c\left)\right(a-b+c\left)\right]$
3. $(b+c)\left[\right(a+b-c\left)\right(a+b+c\left)\right]$
4. $(b+c)\left[\right(a-b+c\left)\right(a-b+c\left)\right]$

Q. Find the value of a using long division method: $\sqrt{x^4+2x^3+5x^2+ax+4}$

1. $2$
2. $3$
3. $4$
4. $1$

Q. Factorise: $27x^3+1$.

1. $(3x-1)(9x^2-3x+1)$
2. $(3x+1)(9x^2-3x+1)$
3. $(3x+1)(9x^2+3x+1)$
4. $(3x-1)(9x^2+3x+1)$

Q. Simplify the square root of the polynomial using factorisation method: $\frac{a^3-b^3}{a-b}$

1. $\sqrt{a^2-ab+b^2}$
2. $\sqrt{a^2+b^2}$
3. $\sqrt{a^2+ab+b^2}$
4. $\sqrt{a+ab+b^2}$

Q.

Complete.
$z^2-2z-48=\left(z-8\right)\left(z+\square \right)$

1. $3$

2. $6$

3. $12$

4. $4$

Q. Factorise : $125a^3+\frac{1}{8}$