May 2026

Factorize the Expression x² – y² – 4xz + 4z² Factorize the following expression : \(x^2 – y^2 – 4xz + 4z^2\) \[ x^2 – y^2 – 4xz + 4z^2 \] \[ = (x^2 – 4xz + 4z^2) – y^2 \] \[ = (x – 2z)^2 – y^2 \] \[ = (x – 2z – […]

Factorize the Expression a² + 4b² – 4ab – 4c² Factorize the following expression : \(a^2 + 4b^2 – 4ab – 4c^2\) \[ a^2 + 4b^2 – 4ab – 4c^2 \] \[ = (a^2 – 4ab + 4b^2) – 4c^2 \] \[ = (a – 2b)^2 – (2c)^2 \] \[ = (a – 2b –

Factorize a² + 2ab + b² – c² Question: Factorize: \[ a^2+2ab+b^2-c^2 \] Solution: \[ a^2+2ab+b^2-c^2 \] \[ =(a+b)^2-c^2 \] \[ =(a+b-c)(a+b+c) \] \[ \boxed{(a+b-c)(a+b+c)} \] Next Question / Full Exercise

Factorize 21x² – 2x + 1/21 Question: Factorize: \[ 21x^2-2x+\frac{1}{21} \] Solution: \[ 21x^2-2x+\frac{1}{21} \] \[ =21x^2-2\left(x\cdot\frac{1}{21}\right)+\frac{1}{21^2}\cdot21 \] \[ =21\left(x^2-\frac{2x}{21}+\frac{1}{441}\right) \] \[ =21\left(x-\frac{1}{21}\right)^2 \] \[ =\left(\sqrt{21}x-\frac{1}{\sqrt{21}}\right)^2 \] \[ \boxed{21\left(x-\frac{1}{21}\right)^2} \] Next Question / Full Exercise

Factorize x(x – 2)(x – 4) + 4x – 8 Question: Factorize: \[ x(x-2)(x-4)+4x-8 \] Solution: \[ x(x-2)(x-4)+4x-8 \] \[ =x(x-2)(x-4)+4(x-2) \] \[ =(x-2)\{x(x-4)+4\} \] \[ =(x-2)(x^2-4x+4) \] \[ =(x-2)(x-2)^2 \] \[ =(x-2)^3 \] \[ \boxed{(x-2)^3} \] Next Question / Full Exercise

Factorize 6ab – b² + 12ac – 2bc Question: Factorize: \[ 6ab-b^2+12ac-2bc \] Solution: \[ 6ab-b^2+12ac-2bc \] \[ =(6ab-b^2)+(12ac-2bc) \] \[ =b(6a-b)+2c(6a-b) \] \[ =(6a-b)(b+2c) \] \[ \boxed{(6a-b)(b+2c)} \] Next Question / Full Exercise

Factorize x³ – 2x²y + 3xy² – 6y³ Question: Factorize: \[ x^3-2x^2y+3xy^2-6y^3 \] Solution: \[ x^3-2x^2y+3xy^2-6y^3 \] \[ =x^2(x-2y)+3y^2(x-2y) \] \[ =(x-2y)(x^2+3y^2) \] \[ \boxed{(x-2y)(x^2+3y^2)} \] Next Question / Full Exercise

Factorize x² + y – xy – x Question: Factorize: \[ x^2+y-xy-x \] Solution: \[ x^2+y-xy-x \] \[ =x^2-x-xy+y \] \[ =x(x-1)-y(x-1) \] \[ =(x-y)(x-1) \] \[ \boxed{(x-y)(x-1)} \] Next Question / Full Exercise

Factorize x(x³ – y³) + 3xy(x – y) Question: Factorize: \[ x(x^3-y^3)+3xy(x-y) \] Solution: \[ x(x^3-y^3)+3xy(x-y) \] \[ =x(x-y)(x^2+xy+y^2)+3xy(x-y) \] \[ =(x-y)\left[x(x^2+xy+y^2)+3xy\right] \] \[ =(x-y)(x^3+x^2y+xy^2+3xy) \] \[ =(x-y)\left(x^3+x^2y+xy^2+y^3-y^3+3xy\right) \] \[ =(x-y)\left[(x+y)(x^2+y^2)+xy(x+y)-y^3+3xy\right] \] \[ =(x-y)(x+y)(x^2+y^2+xy) \] \[ \boxed{(x-y)(x+y)(x^2+xy+y^2)} \] Next Question / Full Exercise

Factorize a²x² + (ax² + 1)x + a Question: Factorize: \[ a^2x^2+(ax^2+1)x+a \] Solution: \[ a^2x^2+(ax^2+1)x+a \] \[ =a^2x^2+ax^3+x+a \] \[ =ax(ax+x^2)+1(x+a) \] \[ =ax(x+a)+1(x+a) \] \[ =(x+a)(ax+1) \] \[ \boxed{(x+a)(ax+1)} \] Next Question / Full Exercise