Question

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which equation is the difference of squares identity:
$(a+b)^2 = a^2 + 2ab +b^2$
$a^3 + b^3 = (a + b)(a^2 - ab + b^2)$
$a^2 - b^2 = (a + b)(a - b)$
$a^3 - b^3 = (a + b)(a^2 - ab + b^2)$

Explanation:

The difference of squares identity refers to factoring the subtraction of two squared terms. Each option is analyzed:

1. $(a+b)^2 = a^2 + 2ab +b^2$ is the square of a sum identity.
2. $a^3 + b^3 = (a + b)(a^2 - ab + b^2)$ is the sum of cubes identity.
3. $a^2 - b^2 = (a + b)(a - b)$ matches the definition of the difference of squares: two squared terms subtracted, factored into a product of sum and difference of the base terms.
4. $a^3 - b^3 = (a + b)(a^2 - ab + b^2)$ is the difference of cubes identity.

Answer:

$\boldsymbol{a^2 - b^2 = (a + b)(a - b)}$