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Factorise x^(4)-y^(4).

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

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Simplify rational expressions

Full solution

Q. Factorise

x^{4}-y^{4}

.

Recognize as Difference of Squares: Recognize the expression $x^4 - y^4$ as a difference of squares. $\newline$ The difference of squares formula is $a^2 - b^2 = (a + b)(a - b)$ . $\newline$ Here, $a^2 = x^4$ and $b^2 = y^4$ , so $a = x^2$ and $b = y^2$ .
Apply Formula to $x^4 - y^4$ : Apply the difference of squares formula to $x^4 - y^4$ . Using the formula from Step $1$ , we get: $x^4 - y^4 = (x^2)^2 - (y^2)^2 = (x^2 + y^2)(x^2 - y^2)$ .
Recognize $x^2 - y^2$ as Difference of Squares: Recognize that $x^2 - y^2$ is also a difference of squares. $\newline$ Using the same formula, $a^2 - b^2 = (a + b)(a - b)$ , with $a = x$ and $b = y$ , we get: $\newline$ $x^2 - y^2 = (x + y)(x - y)$ .
Substitute Factored Form: Substitute the factored form of $x^2 - y^2$ back into the expression from Step $2$ . $\newline$ We now have: $\newline$ $x^4 - y^4 = (x^2 + y^2)(x + y)(x - y).$

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