Question

Factor completely.
8y2–162

Answer 1

To factor the expression \( 8y^2 - 162 \), we can follow these steps:

1. **Factor out the greatest common factor (GCF)**: The GCF of \( 8y^2 \) and \( 162 \) is \( 2 \).
\[
8y^2 - 162 = 2(4y^2 - 81)
\]

2. **Recognize the difference of squares**: The expression \( 4y^2 - 81 \) is a difference of squares, which can be factored using the formula \( a^2 - b^2 = (a - b)(a + b) \). Here, \( a = 2y \) and \( b = 9 \) since \( 4y^2 = (2y)^2 \) and \( 81 = 9^2 \).

\[
4y^2 - 81 = (2y - 9)(2y + 9)
\]

3. **Combine it all together**: Now we substitute back into our expression:
\[
8y^2 - 162 = 2(2y - 9)(2y + 9)
\]

Thus, the completely factored form of the given expression is:
\[
\boxed{2(2y - 9)(2y + 9)}
\]