Question

Which expression is equivalent to the expression (x^2-y^2)^2​

Answer 1

Step-by-step explanation:

$(x^2-y^2)^2\\\\\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\=(x^2)^2-2(x^2)(y^2)+(y^2)^2\\\\\text{use}\ (a^n)^m=a^{nm}\\\\=x^4-2x^2y^2+y^2\\-----------------------------$

$\text{Other solution}\\\\(x^2-y^2)^2\\\\\text{use}\ a^2-b^2=(a-b)(a+b)\\\\= [(x-y)(x+y)]^2\\\\\text{use}\ (ab)^n=a^nb^n\\\\=(x-y)^2(x+y)^2$