Question

which equation is the sum of a square 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:

Step1: Identify sum of squares identity

Recall that the sum of a square (square of sum) identity expands the square of a binomial sum.

Step2: Match with options

Check each option:

• Option1: $(a+b)^2 = a^2 + 2ab + b^2$ is the square of a sum (sum of square terms plus cross term, which is the sum of a square identity).
• Option2: $a^3 + b^3 = (a + b)(a^2 - ab + b^2)$ is sum of cubes.
• Option3: $a^2 - b^2 = (a + b)(a - b)$ is difference of squares.
• Option4: $a^3 - b^3 = (a + b)(a^2 - ab + b^2)$ is incorrect (correct difference of cubes is $(a-b)(a^2+ab+b^2)$).

Answer:

A. $(a+b)^2 = a^2 + 2ab +b^2$