Question

which expression is equivalent to 121x^2 - 64x^2
A. (11x - 16y) (11x + 16y)
B. (11x -16y) (11x - 16y)
C. (11x + 8y) (11x + 8y)
D. (11x + 8y) (11x - 8y)

Answer 1

To simplify the expression \( 121x^2 - 64x^2 \), we first notice that it can be factored.

1. **Combine like terms**:
\[
121x^2 - 64x^2 = (121 - 64)x^2 = 57x^2
\]

Next, it appears there might be some confusion with the original question, as the expression has simplified to \( 57x^2 \) rather than a binomial product. However, if we treat the original expression as \( 121x^2 - 64y^2 \) (which would match a difference of squares), we can factor it accordingly.

2. **Factor as a difference of squares**:
\[
121x^2 - 64y^2 = (11x)^2 - (8y)^2
\]

Using the difference of squares formula \( a^2 - b^2 = (a-b)(a+b) \), where \( a = 11x \) and \( b = 8y \):
\[
(11x - 8y)(11x + 8y)
\]

3. **Now looking at the given choices**:
- A. \( (11x - 16y)(11x + 16y) \)
- B. \( (11x - 16y)(11x - 16y) \)
- C. \( (11x + 8y)(11x + 8y) \)
- D. \( (11x + 8y)(11x - 8y) \)

From the factorization step above, the correct answer is:

**D. \( (11x + 8y)(11x - 8y) \)**

This represents the correct factorization of \( 121x^2 - 64y^2 \).