Which is equivalent to 9y2-4x9y2+4x, and what type of special product is it?A: 81y4-16x2, a perfect square trinomialB: 81y4-16x2, the difference of squaresC: 81y4-72xy2-16x2, a perfect square trinomialD: 81y4-72xy2-16x2, the difference of squares

Answer:Option B: 81y^4-16x^2, the difference of squareswe know that The Difference of Squares is two terms that are squa and separated by a subtraction signso\((a+b)(a-b)=(a^{}2{}-b^{}2{})\)In this problem we have\((9y^{}2{}-4x)(9y^{}2{}+4x)\)Let\(a=9y^{}2{}\)\(b=4x\)so\(a^{}2{}=(9y^{}2{})^{}2{}=81y^{}4{}\)\(b^{}2{}=(4x)^{}2{}=16x^{}2{}\)substitute\((9y^{}2{}-4x)(9y^{}2{}+4x)=81y^{}4{}-16x^{}2{}\)