Final answer:
Expressions equivalent to 162x^2 - 72 are 2(81x^2 - 36), 2(9x - 6)(9x + 6), and 18(3x - 2)(3x + 2) because they simplify directly to the original expression or represent a difference of squares that expands to the original expression.
Step-by-step explanation:
The question asks to select all expressions equivalent to 162x^2 – 72. We will review each option to determine which are equivalent:
- 2(9x - 6)^2: Expanding this expression, we get 2(81x^2 - 108x + 36), which is not equivalent because it includes an x term and the constant differs.
- 2(81x^2 – 36): This expression simplifies directly to 162x^2 - 72, so it is equivalent.
- 2(9x - 6)(9x + 6): This is the difference of squares and expands to 162x^2 - 72, which is equivalent.
- 18(3x^2 – 2)^2: Expanding this expression results in a term with x and a varying constant, making it not equivalent.
- 18(3x - 2)(3x + 2): Similar to the previous option, this is a difference of squares that simplifies to 162x^2 - 72, so it is equivalent.
Thus, the expressions equivalent to 162x^2 - 72 are 2(81x^2 – 36), 2(9x - 6)(9x + 6), and 18(3x - 2)(3x + 2).