Factorize the Expression 8a³ – b³ – 4ax + 2bx Factorize the following expression : \(8a^3 – b^3 – 4ax + 2bx\) \[ 8a^3 – b^3 – 4ax + 2bx \] \[ = (2a)^3 – b^3 – 2x(2a – b) \] \[ = (2a – b)(4a^2 + 2ab + b^2) – 2x(2a – b) \] […]

Factorize the Expression a³ + 3a²b + 3ab² + b³ – 8 Factorize the following expression : \(a^3 + 3a^2b + 3ab^2 + b^3 – 8\) \[ a^3 + 3a^2b + 3ab^2 + b^3 – 8 \] \[ = (a + b)^3 – 2^3 \] \[ = (a + b – 2) \left[(a + b)^2

Factorize the Expression a³ – 1/a³ – 2a + 2/a Factorize the following expression : \(a^3 – \frac{1}{a^3} – 2a + \frac{2}{a}\) \[ a^3 – \frac{1}{a^3} – 2a + \frac{2}{a} \] \[ = \left(a^3 – \frac{1}{a^3}\right) – 2\left(a – \frac{1}{a}\right) \] \[ = \left(a – \frac{1}{a}\right)\left(a^2 + 1 + \frac{1}{a^2}\right) – 2\left(a – \frac{1}{a}\right) \]

Factorize the Expression x³ + 6x² + 12x + 16 Factorize the following expression : \(x^3 + 6x^2 + 12x + 16\) \[ x^3 + 6x^2 + 12x + 16 \] \[ = x^3 + 2^3 + 6x^2 + 12x \] \[ = (x + 2)(x^2 – 2x + 4) + 6x(x + 2) \]

Factorize the Expression a¹² + b¹² Factorize the following expression : \(a^{12} + b^{12}\) \[ a^{12} + b^{12} \] \[ = (a^4)^3 + (b^4)^3 \] \[ = (a^4 + b^4)(a^8 – a^4b^4 + b^8) \] Next Question / Full Exercise

Factorize the Expression (x + 2)³ + (x – 2)³ Factorize the following expression : \((x + 2)^3 + (x – 2)^3\) \[ (x + 2)^3 + (x – 2)^3 \] \[ = \left[(x + 2) + (x – 2)\right] \left[(x + 2)^2 – (x + 2)(x – 2) + (x – 2)^2\right] \] \[

Factorize the Expression (a + b)³ – 8(a – b)³ Factorize the following expression : \((a + b)^3 – 8(a – b)^3\) \[ (a + b)^3 – 8(a – b)^3 \] \[ = (a + b)^3 – [2(a – b)]^3 \] \[ = \left[(a + b) – 2(a – b)\right] \left[(a + b)^2 + 2(a

Simplify (1.2³ – 0.2³)/(1.2² + 1.2×0.2 + 0.2²) Simplify : \(\dfrac{1.2 \times 1.2 \times 1.2 – 0.2 \times 0.2 \times 0.2}{1.2 \times 1.2 + 1.2 \times 0.2 + 0.2 \times 0.2}\) \[ \frac{1.2^3 – 0.2^3}{1.2^2 + 1.2 \times 0.2 + 0.2^2} \] \[ = \frac{a^3 – b^3}{a^2 + ab + b^2} \] \[ = \frac{(a

Simplify (155³ – 55³)/(155² + 155×55 + 55²) Simplify : \(\dfrac{155 \times 155 \times 155 – 55 \times 55 \times 55}{155 \times 155 + 155 \times 55 + 55 \times 55}\) \[ \frac{155^3 – 55^3}{155^2 + 155 \times 55 + 55^2} \] \[ = \frac{a^3 – b^3}{a^2 + ab + b^2} \] \[ = \frac{(a

Simplify (173³ + 127³)/(173² – 173×127 + 127²) Simplify : \(\dfrac{173 \times 173 \times 173 + 127 \times 127 \times 127}{173 \times 173 – 173 \times 127 + 127 \times 127}\) \[ \frac{173^3 + 127^3}{173^2 – 173 \times 127 + 127^2} \] \[ = \frac{a^3 + b^3}{a^2 – ab + b^2} \] \[ = \frac{(a