Question

which will result in a difference of squares?
(-7x + 4)(-7x + 4)
(-7x + 4)(4 - 7x)
(-7x + 4)(-7x - 4)
(-7x + 4)(7x - 4)

Explanation:

Step1: Recall the difference of squares formula

The difference of squares formula is \( (a + b)(a - b)=a^2 - b^2 \). We need to identify which pair of binomials fits this form, where one binomial is \( a + b \) and the other is \( a - b \).

Step2: Analyze each option

• Option 1: \( (-7x + 4)(-7x + 4)=(-7x + 4)^2 \), which is a perfect square trinomial (since it's \( (a + b)^2 \) with \( a=-7x \), \( b = 4 \)), not a difference of squares.
• Option 2: \( (-7x + 4)(4 - 7x)=(-7x + 4)(-7x + 4)=(-7x + 4)^2 \), same as option 1, a perfect square trinomial.
• Option 3: \( (-7x + 4)(-7x - 4) \). Let \( a=-7x \) and \( b = 4 \). Then this is \( (a + b)(a - b) \) (since \( (a + b)(a - b)=a^2 - b^2 \), here \( a=-7x \), \( b = 4 \), so \( (-7x)^2-4^2 = 49x^2 - 16 \), which is a difference of squares.
• Option 4: \( (-7x + 4)(7x - 4)=-(7x - 4)(7x - 4)=-(7x - 4)^2 \), a perfect square trinomial (negative of a square), not a difference of squares.

Answer:

\( (-7x + 4)(-7x - 4) \) (the third option)