Question

Which products result in a difference of squares? Check all that apply.(x – y)(y – x)(6 – y)(6 – y)(3 + xz)(–3 + xz)(y2 – xy)(y2 + xy)(25x – 7y)(–7y + 25x)(64y2 + x2)(–x2 + 64y2)

Answer 1

1. (3 + xz)(–3 + xz)

2. (y² – xy)(y² + xy)

3. (64y2 + x2)(–x2 + 64y2)

Step-by-step explanation

The difference of 2 squares is in the form (a+b)(a-c).

(3 + xz)(–3 + xz) = (3 + xz)(xz -3)

= (xz + 3)(xz - 3)

= x²y²-3xy+3xy-9

=x²y² - 3²

(y² – xy)(y² + xy) = y⁴+xy³-xy³-x²y²

= y⁴ - x²y²

(64y2 + x2)(–x2 + 64y2)= (64y²+x²)(64y²-x²)

= 4096y⁴-64y²x²+64y²x²-x⁴

= 4096y⁴ - x⁴