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

Factorize the Expression x² – 3x – 6 Factorize the following expression : \(x^2 – 3x – 6\) \[ x^2 – 3x – 6 \] \[ = x^2 – \frac{3 + \sqrt{33}}{2}x + \frac{-3 + \sqrt{33}}{2}x – 6 \] \[ = x\left(x – \frac{3 + \sqrt{33}}{2}\right) + \frac{-3 + \sqrt{33}}{2} \left(x – \frac{3 + \sqrt{33}}{2}\right)

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

Factorize the Expression x² + 6√2x + 10 Factorize the following expression : \(x^2 + 6\sqrt{2}x + 10\) \[ x^2 + 6\sqrt{2}x + 10 \] \[ = x^2 + 5\sqrt{2}x + \sqrt{2}x + 10 \] \[ = x(x + 5\sqrt{2}) + \sqrt{2}(x + 5\sqrt{2}) \] \[ = (x + 5\sqrt{2})(x + \sqrt{2}) \] Next Question

Factorize the Expression x⁴ + x²y² + y⁴ Factorize the following expression : \(x^4 + x^2y^2 + y^4\) \[ x^4 + x^2y^2 + y^4 \] \[ = x^4 + 2x^2y^2 + y^4 – x^2y^2 \] \[ = (x^2 + y^2)^2 – (xy)^2 \] \[ = (x^2 + y^2 – xy)(x^2 + y^2 + xy) \]

Factorize the Expression xy⁹ – yx⁹ Factorize the following expression : \(xy^9 – yx^9\) \[ xy^9 – yx^9 \] \[ = xy(y^8 – x^8) \] \[ = xy(y^4 – x^4)(y^4 + x^4) \] \[ = xy(y^2 – x^2)(y^2 + x^2)(y^4 + x^4) \] \[ = xy(y – x)(y + x)(x^2 + y^2)(x^4 + y^4) \]