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

Factorize the Expression 54x⁶y + 2x³y⁴ Factorize the following expression : \(54x^6y + 2x^3y^4\) \[ 54x^6y + 2x^3y^4 \] \[ = 2x^3y(27x^3 + y^3) \] \[ = 2x^3y\left[(3x)^3 + y^3\right] \] \[ = 2x^3y(3x + y)(9x^2 – 3xy + y^2) \] Next Question / Full Exercise

Factorize the Expression 10x⁴y – 10xy⁴ Factorize the following expression : \(10x^4y – 10xy^4\) \[ 10x^4y – 10xy^4 \] \[ = 10xy(x^3 – y^3) \] \[ = 10xy(x – y)(x^2 + xy + y^2) \] Next Question / Full Exercise

Factorize the Expression x³/216 – 8y³ Factorize the following expression : \(\frac{x^3}{216} – 8y^3\) \[ \frac{x^3}{216} – 8y^3 \] \[ = \left(\frac{x}{6}\right)^3 – (2y)^3 \] \[ = \left(\frac{x}{6} – 2y\right) \left[\left(\frac{x}{6}\right)^2 + \left(\frac{x}{6}\right)(2y) + (2y)^2\right] \] \[ = \left(\frac{x}{6} – 2y\right) \left(\frac{x^2}{36} + \frac{xy}{3} + 4y^2\right) \] Next Question / Full Exercise