Educational

Factorize 8x^3 + 27y^3 + 36x^2y + 54xy^2 Factorize : \( 8x^3 + 27y^3 + 36x^2y + 54xy^2 \) \[ 8x^3 + 27y^3 + 36x^2y + 54xy^2 \] \[ = 8x^3 + 36x^2y + 54xy^2 + 27y^3 \] \[ = (2x)^3 + 3(2x)^2(3y) + 3(2x)(3y)^2 + (3y)^3 \] \[ = (2x + 3y)^3 \] Next […]

Factorize 8/27x^3 + 1 + 4/3x^2 + 2x Factorize : \( \frac{8}{27}x^3 + 1 + \frac{4}{3}x^2 + 2x \) \[ \frac{8}{27}x^3 + 1 + \frac{4}{3}x^2 + 2x \] \[ = \frac{8}{27}x^3 + \frac{4}{3}x^2 + 2x + 1 \] \[ = \left(\frac{2x}{3}\right)^3 + 3\left(\frac{2x}{3}\right)^2(1) + 3\left(\frac{2x}{3}\right)(1)^2 + 1^3 \] \[ = \left(\frac{2x}{3} + 1\right)^3 \] Next

Factorize 125x^3 – 27y^3 – 255x^2y + 135xy^2 Factorize : \( 125x^3 – 27y^3 – 255x^2y + 135xy^2 \) \[ 125x^3 – 27y^3 – 255x^2y + 135xy^2 \] \[ = 125x^3 – 255x^2y + 135xy^2 – 27y^3 \] \[ = (5x)^3 – 3(5x)^2(3y) + 3(5x)(3y)^2 – (3y)^3 \] \[ = (5x – 3y)^3 \] Next

Factorize 64a^3 + 125b^3 + 240a^2b + 300ab^2 Factorize : \( 64a^3 + 125b^3 + 240a^2b + 300ab^2 \) \[ 64a^3 + 125b^3 + 240a^2b + 300ab^2 \] \[ = 64a^3 + 240a^2b + 300ab^2 + 125b^3 \] \[ = (4a)^3 + 3(4a)^2(5b) + 3(4a)(5b)^2 + (5b)^3 \] \[ = (4a + 5b)^3 \] Next

Simplify (2x – 5y)³ – (2x + 5y)³ Simplify : \((2x – 5y)^3 – (2x + 5y)^3\) \[ (2x – 5y)^3 – (2x + 5y)^3 \] \[ = \left[(2x – 5y) – (2x + 5y)\right] \left[(2x – 5y)^2 + (2x – 5y)(2x + 5y) + (2x + 5y)^2\right] \] \[ = (-10y) \left[(4x^2 – 20xy

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