Question

factor the expression completely.\\(x^{5}y^{4}-y^{4}\\)

Explanation:

Step1: Factor out common term

$x^5y^4 - y^4 = y^4(x^5 - 1)$

Step2: Factor difference of fifth powers

Use $a^5 - b^5=(a-b)(a^4+a^3b+a^2b^2+ab^3+b^4)$, here $a=x,b=1$:
$x^5 - 1=(x-1)(x^4+x^3+x^2+x+1)$

Step3: Combine factored terms

Substitute back into the expression.

Answer:

$y^4(x-1)(x^4+x^3+x^2+x+1)$