May 2026

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

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

Factorize the Expression x⁴y⁴ – xy Factorize the following expression : \(x^4y^4 – xy\) \[ x^4y^4 – xy \] \[ = xy(x^3y^3 – 1) \] \[ = xy\left[(xy)^3 – 1^3\right] \] \[ = xy(xy – 1)(x^2y^2 + xy + 1) \] Next Question / Full Exercise

Factorize the Expression x³y³ + 1 Factorize the following expression : \(x^3y^3 + 1\) \[ x^3y^3 + 1 \] \[ = (xy)^3 + 1^3 \] \[ = (xy + 1)(x^2y^2 – xy + 1) \] Next Question / Full Exercise

Factorize the Expression 1029 – 3x³ Factorize the following expression : \(1029 – 3x^3\) \[ 1029 – 3x^3 \] \[ = 3(343 – x^3) \] \[ = 3(7^3 – x^3) \] \[ = 3(7 – x)(49 + 7x + x^2) \] Next Question / Full Exercise

Factorize the Expression 8x²y³ – x⁵ Factorize the following expression : \(8x^2y^3 – x^5\) \[ 8x^2y^3 – x^5 \] \[ = x^2(8y^3 – x^3) \] \[ = x^2\left[(2y)^3 – x^3\right] \] \[ = x^2(2y – x)(4y^2 + 2xy + x^2) \] Next Question / Full Exercise

Factorize the Expression (a – 2b)³ – 512b³ Factorize the following expression : \((a – 2b)^3 – 512b^3\) \[ (a – 2b)^3 – 512b^3 \] \[ = (a – 2b)^3 – (8b)^3 \] \[ = \left[(a – 2b) – 8b\right] \left[(a – 2b)^2 + 8b(a – 2b) + (8b)^2\right] \] \[ = (a – 10b)

Factorize the Expression 32a³ + 108b³ Factorize the following expression : \(32a^3 + 108b^3\) \[ 32a^3 + 108b^3 \] \[ = 4(8a^3 + 27b^3) \] \[ = 4\left[(2a)^3 + (3b)^3\right] \] \[ = 4(2a + 3b)(4a^2 – 6ab + 9b^2) \] Next Question / Full Exercise