Question

Which of the following expressions is equivalent to \(2 a(a\) \(\left.-3 b^2\right)+a^2 ?\) A. \(2 a^2-6 a b^2\) B. \(3 a^2-3 b^2\) C. \(2 a\left(a-3 b^2\right)\) D. \(3 a\left(a-2 b^2\right)\)

Short answer

The short answer is A: \(3a^2 - 6ab^2\).

Step-by-step solution

Distribute the constant in the expression

First, distribute the 2 inside the parenthesis: \[2a(a - 3b^2) + a^2 = 2a^2 - 6ab^2 + a^2\]

Combine like terms

Now, combine the like terms (both of which are \(a^2\)): \[2a^2 - 6ab^2 + a^2 = 3a^2 - 6ab^2\]

Compare the simplified expression with given options

Compare the simplified expression \(3a^2 - 6ab^2\) with the given options: A. \(2 a^2 - 6 a b^2\) B. \(3 a^2 - 3 b^2\) C. \(2 a(a - 3 b^2)\) D. \(3 a(a - 2 b^2)\) Our simplified expression matches option A, so the correct answer is A: \(2 a^2 - 6 a b^2\).