Divide $2 x^{3 a} - 6 x^{2 a} y^{a} + 6 x^{a} y^{2 a} - 2 y^{3 a}$ by $2 x^{a} - 2 y^{a}$ [4 MARKS]

Open in App

Solution

Concept: 1 Mark
Application: 3 Marks

$2 x^{3 a} - 6 x^{2 a} y^{a} + 6 x^{a} y^{2 a} - 2 y^{3 a}$

$= 2 (x^{3 a} - 3 x^{2 a} y^{a} + 3 x^{a} y^{2 a} - y^{3 a})$

$= 2 {(x^{a})^{3} - (y^{a})^{3} - 3 x^{a} y^{a} (x^{a} - y^{a})} [∵ x^{3 a} = (x^{a})^{3} a n d y^{3 a} = (y^{a})^{3}]$

$U s i n g t h e i d e n t i t y a^{3} - b^{3} - 3 a b (a - b) = (a - b)^{3}$

$= 2 (x^{a} - y^{a})^{3}$

$2 x^{a} - 2 y^{a} = 2 (x^{a} - y^{a})$

$∴ \frac{2 x^{3 a} - 6 x^{2 a} y^{a} + 6 x^{a} y^{2 a} - 2 y^{3 a}}{2 x^{a} - 2 y^{a}} = \frac{2 (x^{a} - y^{a})^{3}}{2 (x^{a} - y^{a})}$

$= (x^{a} - y^{a})^{2}$

Suggest Corrections

Similar questions

Divide $(x^{2} + 3) (x^{2} - 3) + 9$ by $x^{4}$ [1 MARK]

x, y, z

∣ ∣ ∣ ∣ \begin{matrix} a + 2 & a + 3 & a + 2 x a + 3 & a + 4 & a + 2 y a + 4 & a + 5 & a + 2 z \end{matrix} ∣ ∣ ∣ ∣

44 (x^{4} - 5 x^{3} - 24 x^{2})

11 x (x - 8)

x^{4 a} + x^{2 a} y^{2 b} + y^{4 b}

x^{2 a} + x^{a} y^{b} + y^{2 b}

3

4

Join BYJU'S Learning Program