Factorise $x^{4} + 4 y^{4}$ .

Open in App

Solution

Here again we add and subtract suitable terms to bring it in a factorisation form. Notice that
$x^{4} + 4 y^{4} = {(x^{2})}^{2} + {({2 y}^{2})}^{2} - 2 (x^{2}) ({2 y}^{2}) - {(2 x y)}^{2} = {(x^{2} + {2 y}^{2})}^{2} - {(2 x y)}^{2}$
The second expression is in the form $a^{2} - b^{2}$ , where $a = (x^{2} + 2 y^{2})$ and $b = 2 x y$
Hence we may write
$x^{4} + 4 y^{4} = (x^{2} + {2 y}^{2} + 2 x y) (x^{2} + {2 y}^{2} - 2 x y)$

Suggest Corrections

Similar questions

Factorise x⁴ + 4y⁴. Use this to prove that 2011⁴ + 64 is a composite number.

{(3 x - 4 y)}^{4} - x^{4}

(x^{4} + 4 y^{4})

Question 57 (e)

Add the following expression:

$x^{3} y^{2} + x^{2} y^{3} + 3 y^{4} a n d x^{4} + 3 x^{2} y^{3} + 4 y^{4}$

Join BYJU'S Learning Program