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

Hey there!

A difference of squares is the product of two binomials that when multiplied out, don't have any b term. Remember, quadratic trinomials are written asL

ax^2 + bx + c

A difference of squares is always one factor plus a number, times the same factor minus a number. For example:

(x + 3)(x - 3) = x^2 -3x + 3x - 9 = x^2 - 9

Notice how it does not have a b term.

1) For the first one, we know we don't have a difference of squares because even though the factors look similar, the -5z is the opposite of the original factor, and therefore it doesn't work.

2) For the next, we know we have a difference of squares because it's the same factor (w) plus another number times the same factor minus the same number (2.5).

 3) The next one we know isn't a difference of squares because there's no term being subtracted.

4) This one would be a difference of squares because we have the factor of -4 -9, and the -4 + 9. If we multiply them out, we get:

(-4v-9)(-4v+9) = 16v^2 - 36v + 36v - 81 = 16v^2 - 81

Notice how here, the b term is gone.

5) This one cannot be a difference of squares because there's no identical factor that's being multiplied, so even if it was plus and minus the same factor, it would not work.

6) For this final one, we know that it can't be a difference of squares because there's no +5, it's only a minus twice. If we multiply, we get: p^2 -10p + 25.

Therefore, your answers are the second one, and the fourth one.

For future references, differences of squares are part of special binomial products. 

Hope this helps!