To find the expression equivalent to [tex]\((-6 a b)^2\)[/tex], let's go through the problem step by step.
1. Understand the expression: The given expression is [tex]\((-6 a b)^2\)[/tex]. This means that we are squaring the expression [tex]\(-6 a b\)[/tex].
2. Square the expression: Squaring an expression means multiplying the expression by itself. Therefore, we have:
[tex]\[
(-6 a b) \times (-6 a b)
\][/tex]
3. Multiply the coefficients: First, we square the numerical coefficient [tex]\(-6\)[/tex]:
[tex]\[
(-6) \times (-6) = 36
\][/tex]
4. Multiply the variables: Next, we square each variable in the expression individually:
[tex]\[
(a \times a) = a^2
\][/tex]
[tex]\[
(b \times b) = b^2
\][/tex]
5. Combine the results: Putting it all together, we multiply the squared coefficient by the squared variables:
[tex]\[
36 \times a^2 \times b^2 = 36 a^2 b^2
\][/tex]
So, the expression [tex]\((-6 a b)^2\)[/tex] simplifies to [tex]\(36 a^2 b^2\)[/tex].
Among the answer choices:
- A. [tex]\(-36 a^2 b^2\)[/tex] is incorrect because the coefficient is negative.
- B. [tex]\(36 a^2 b^2\)[/tex] is correct because it matches our simplified expression.
- C. [tex]\(-12 a^2 b^2\)[/tex] is incorrect because both the coefficient and exponent values do not match.
- D. [tex]\(-12 a b^2\)[/tex] is incorrect because both the coefficient and the exponent values do not match.
Therefore, the correct answer is:
B. [tex]\(36 a^2 b^2\)[/tex]
