Question

which products result in a difference of squares? check all that apply. (5x + 3)(-5x - 3) (w - 2.5)(w + 2.5) (8y + 1)(8y + 1) (-4v - 9)(-4v + 9) (6y + 7)(7y - 6) (p - 5)(p - 5)

Explanation:

Step1: Recall difference of squares rule

A product of the form $(a+b)(a-b)$ or $(a-b)(a+b)$ equals $a^2 - b^2$, a difference of squares.

Step2: Analyze $(5z+3)(-5z-3)$

Factor out $-1$: $-(5z+3)(5z+3)=-(5z+3)^2$, a perfect square, not difference of squares.

Step3: Analyze $(w-2.5)(w+2.5)$

Matches $(a-b)(a+b)$ where $a=w$, $b=2.5$.
Expression: $w^2 - (2.5)^2 = w^2 - 6.25$

Step4: Analyze $(8g+1)(8g+1)$

This is $(8g+1)^2$, a perfect square, not difference of squares.

Step5: Analyze $(-4v-9)(-4v+9)$

Matches $(a-b)(a+b)$ where $a=-4v$, $b=9$.
Expression: $(-4v)^2 - 9^2 = 16v^2 - 81$

Step6: Analyze $(6y+7)(7y-6)$

Terms are not identical binomials with opposite signs, so no difference of squares.

Step7: Analyze $(p-5)(p-5)$

This is $(p-5)^2$, a perfect square, not difference of squares.

Answer:

• $(w - 2.5)(w + 2.5)$
• $(-4v - 9)(-4v + 9)$