Educational

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

Factorize the Expression 5√5x² + 20x + 3√5 Factorize the following expression : \(5\sqrt{5}x^2 + 20x + 3\sqrt{5}\) \[ 5\sqrt{5}x^2 + 20x + 3\sqrt{5} \] \[ = 5\sqrt{5}x^2 + 15x + 5x + 3\sqrt{5} \] \[ = 5x(\sqrt{5}x + 1) + 3\sqrt{5}(\sqrt{5}x + 1) \] \[ = (\sqrt{5}x + 1)(5x + 3\sqrt{5}) \] Next Question

Factorize the Expression x² + 2√3x – 24 Factorize the following expression : \(x^2 + 2\sqrt{3}x – 24\) \[ x^2 + 2\sqrt{3}x – 24 \] \[ = x^2 + 6\sqrt{3}x – 4\sqrt{3}x – 24 \] \[ = x(x + 6\sqrt{3}) – 4\sqrt{3}(x + 6\sqrt{3}) \] \[ = (x + 6\sqrt{3})(x – 4\sqrt{3}) \] Next Question

Factorize the Expression x² + 5√5x + 30 Factorize the following expression : \(x^2 + 5\sqrt{5}x + 30\) \[ x^2 + 5\sqrt{5}x + 30 \] \[ = x^2 + 2\sqrt{5}x + 3\sqrt{5}x + 30 \] \[ = x(x + 2\sqrt{5}) + 3\sqrt{5}(x + 2\sqrt{5}) \] \[ = (x + 2\sqrt{5})(x + 3\sqrt{5}) \] Next Question