Factorise: $x^{4} + x^{2} y^{2} + y^{4}$

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Solution

$x^{4} + x^{2} y^{2} + y^{4}$
Adding and Subtracting $x^{2} y^{2}$ from the equation, we get:
$x^{4} + x^{2} y^{2} + y^{4} + x^{2} y^{2} - x^{2} y^{2}$
= $[(x^{2})^{2} + 2 x^{2} y^{2} + (y^{2})^{2}] - x^{2} y^{2}$
= $(x^{2} + y^{2})^{2} - x^{2} y^{2}$

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Similar questions

Question 92 (xxviii)

Factorise the following using the identity $a^{2} - b^{2} = (a + b) (a - b) .$

$x^{4} - y^{4} + x^{2} - y^{2}$

(x^{2} - y^{2}) : (x^{2} + y^{2})

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

\frac{x^{4} - y^{4}}{x^{2} + y^{2}}

Divide $x^{4} - y^{4}$ by $x^{2} - y^{2}$ .

Factorize

i) x⁴ - y⁴+ x²- y²

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