Educational

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

Factorize the Expression 64a³ – b³ Factorize the following expression : \(64a^3 – b^3\) \[ 64a^3 – b^3 \] \[ = (4a)^3 – b^3 \] \[ = (4a – b)\left[(4a)^2 + (4a)b + b^2\right] \] \[ = (4a – b)(16a^2 + 4ab + b^2) \] Next Question / Full Exercise

Factorize the Expression 8x³y³ + 27a³ Factorize the following expression : \(8x^3y^3 + 27a^3\) \[ 8x^3y^3 + 27a^3 \] \[ = (2xy)^3 + (3a)^3 \] \[ = (2xy + 3a)\left[(2xy)^2 – (2xy)(3a) + (3a)^2\right] \] \[ = (2xy + 3a)(4x^2y^2 – 6axy + 9a^2) \] Next Question / Full Exercise

Factorize the Expression 1 – 27a³ Factorize the following expression : \(1 – 27a^3\) \[ 1 – 27a^3 \] \[ = 1^3 – (3a)^3 \] \[ = (1 – 3a)(1^2 + 1 \cdot 3a + (3a)^2) \] \[ = (1 – 3a)(1 + 3a + 9a^2) \] Next Question / Full Exercise

Factorize the Expression y³ + 125 Factorize the following expression : \(y^3 + 125\) \[ y^3 + 125 \] \[ = y^3 + 5^3 \] \[ = (y + 5)(y^2 – 5y + 25) \] Next Question / Full Exercise

Factorize the Expression (x² + 1/x²) – 4(x + 1/x) + 6 Factorize the following expression : \(\left(x^2 + \frac{1}{x^2}\right) – 4\left(x + \frac{1}{x}\right) + 6\) \[ \left(x^2 + \frac{1}{x^2}\right) – 4\left(x + \frac{1}{x}\right) + 6 \] \[ = \left(x + \frac{1}{x}\right)^2 – 2 – 4\left(x + \frac{1}{x}\right) + 6 \] \[ = \left(x +