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 +

Factorize the Expression (x + 2)(x² + 25) – 10x² – 20x Factorize the following expression : \((x + 2)(x^2 + 25) – 10x^2 – 20x\) \[ (x + 2)(x^2 + 25) – 10x^2 – 20x \] \[ = (x + 2)(x^2 + 25) – 10x(x + 2) \] \[ = (x + 2)\left[(x^2 +

Factorize the Expression a² + b² + 2(ab + bc + ca) Factorize the following expression : \(a^2 + b^2 + 2(ab + bc + ca)\) \[ a^2 + b^2 + 2(ab + bc + ca) \] \[ = a^2 + b^2 + 2ab + 2bc + 2ca \] \[ = (a + b)^2 +

Factorize the Expression 4(x – y)² – 12(x – y)(x + y) + 9(x + y)² Factorize the following expression : \(4(x – y)^2 – 12(x – y)(x + y) + 9(x + y)^2\) \[ 4(x – y)^2 – 12(x – y)(x + y) + 9(x + y)^2 \] \[ = [2(x – y)]^2 –

Factorize the Expression 2(x + y)² – 9(x + y) – 5 Factorize the following expression : \(2(x + y)^2 – 9(x + y) – 5\) \[ 2(x + y)^2 – 9(x + y) – 5 \] \[ \text{Let } (x + y) = t \] \[ = 2t^2 – 9t – 5 \] \[

Factorize the Expression 7(x – 2y)² – 25(x – 2y) + 12 Factorize the following expression : \(7(x – 2y)^2 – 25(x – 2y) + 12\) \[ 7(x – 2y)^2 – 25(x – 2y) + 12 \] \[ \text{Let } (x – 2y) = t \] \[ = 7t^2 – 25t + 12 \] \[

Factorize the Expression 2a² + 2√6ab + 3b² Factorize the following expression : \(2a^2 + 2\sqrt{6}ab + 3b^2\) \[ 2a^2 + 2\sqrt{6}ab + 3b^2 \] \[ = (\sqrt{2}a)^2 + 2(\sqrt{2}a)(\sqrt{3}b) + (\sqrt{3}b)^2 \] \[ = (\sqrt{2}a + \sqrt{3}b)^2 \] Next Question / Full Exercise

Factorize the Expression 2x² + 3√5x + 5 Factorize the following expression : \(2x^2 + 3\sqrt{5}x + 5\) \[ 2x^2 + 3\sqrt{5}x + 5 \] \[ = 2x^2 + \sqrt{5}x + 2\sqrt{5}x + 5 \] \[ = x(2x + \sqrt{5}) + \sqrt{5}(2x + \sqrt{5}) \] \[ = (2x + \sqrt{5})(x + \sqrt{5}) \] Next Question