Educational

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 : \(xy^9 – yx^9\) \[ xy^9 – yx^9 \] \[ = xy(y^8 – x^8) \] \[ = xy(y^4 – x^4)(y^4 + x^4) \] \[ = xy(y^2 – x^2)(y^2 + x^2)(y^4 + x^4) \] \[ = xy(y – x)(y + x)(x^2 + y^2)(x^4 + y^4) \]

Factorize the Expression a² – b² + 2bc – c² Factorize the following expression : \(a^2 – b^2 + 2bc – c^2\) \[ a^2 – b^2 + 2bc – c^2 \] \[ = a^2 – (b^2 – 2bc + c^2) \] \[ = a^2 – (b – c)^2 \] \[ = (a – b +

Dimensions of a Cuboid Having Volume 3x² – 12x What are the possible expressions for the dimensions of the cuboid whose volume is : \(3x^2 – 12x\) \[ 3x^2 – 12x \] \[ = 3x(x – 4) \] \[ = 3 \times x \times (x – 4) \] \[ \therefore \] \[ \text{Possible dimensions are

Length and Breadth of Rectangle Having Area 35y² + 13y – 12 Give possible expressions for the length and breadth of rectangle having area : \(35y^2 + 13y – 12\) \[ 35y^2 + 13y – 12 \] \[ = 35y^2 + 28y – 15y – 12 \] \[ = 7y(5y + 4) – 3(5y +

Factorize the Expression (a – b + c)² + (b – c + a)² + 2(a – b + c)(b – c + a) Factorize the following expression : \((a – b + c)^2 + (b – c + a)^2 + 2(a – b + c)(b – c + a)\) \[ (a – b +

Factorize the Expression x² + 12/35x + 1/35 Factorize the following expression : \(x^2 + \frac{12}{35}x + \frac{1}{35}\) \[ x^2 + \frac{12}{35}x + \frac{1}{35} \] \[ = x^2 + \frac{5}{35}x + \frac{7}{35}x + \frac{1}{35} \] \[ = x\left(x + \frac{1}{7}\right) + \frac{1}{5}\left(x + \frac{1}{7}\right) \] \[ = \left(x + \frac{1}{7}\right)\left(x + \frac{1}{5}\right) \] Next Question