Question

which expressions represent a difference of squares?
4x^2 - 12x + 9
3x^2 - 9
49x^2 + 4
25x^2 - 36
1 - 16x^2

Explanation:

Step1: Recall difference - of - squares formula

The difference - of - squares formula is $a^{2}-b^{2}=(a + b)(a - b)$.

Step2: Analyze each expression

• For $4x^{2}-12x + 9=(2x - 3)^{2}$, it is a perfect - square trinomial, not a difference of squares.
• For $3x^{2}-9 = 3(x^{2}-3)$, since $3$ is not a perfect square in the context of the difference - of - squares formula for this binomial form, it is not a difference of squares.
• For $49x^{2}+4$, it is a sum of squares, not a difference of squares.
• For $25x^{2}-36=(5x)^{2}-6^{2}$, here $a = 5x$ and $b = 6$, so it is a difference of squares.
• For $1-16x^{2}=1^{2}-(4x)^{2}$, here $a = 1$ and $b = 4x$, so it is a difference of squares.

Answer:

$25x^{2}-36$, $1 - 16x^{2}$