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

The right answer for the question that is being asked and shown above is that: "(3 + xz)(–3 + xz); (y2 – xy)(y2 + xy); (64y2 + x2)(–x2 + 64y2)." The products that will result to a difference of squares include (3 + xz)(–3 + xz); (y2 – xy)(y2 + xy); (64y2 + x2)(–x2 + 64y2)

Answer 2

Answers
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