Question

Which is equivalent to (9y^2-4x)(9y^2+4x), and what type of special product is it?

Answer 1

$\text{Use:}\ (a-b)(a+b)=a^2-b^2\\\\(a\cdot b)^n=a^n\cdot b^n\\\\(a^n)^m=a^{nm}$


$(9y^2-4x)(9y^2+4x)=(9y^2)^2-(4x)^2=9^2(y^2)^2-4^2x^2\\\\=81y^4-16x^2$

It is the product of the sum by the difference of the same monomials