Question

which expression is equivalent to 121x^2 - 64x^2
(11x - 16y) (11x + 16y)
(11x -16y) (11x - 16y)
(11x + 8y) (11x + 8y)
(11x + 8y) (11x - 8y)

Answers

Answered by GPT-4o mini
To simplify the expression \(121x^2 - 64y^2\), we can observe that it fits the form of a difference of squares, which is given by the formula:

\[
a^2 - b^2 = (a - b)(a + b)
\]

Here, we can identify:

- \(a^2 = 121x^2\) which means \(a = 11x\)
- \(b^2 = 64y^2\) which means \(b = 8y\)

Now we can apply the difference of squares formula:

\[
121x^2 - 64y^2 = (11x)^2 - (8y)^2 = (11x - 8y)(11x + 8y)
\]

Now, looking at the options you provided:

1. \((11x - 16y)(11x + 16y)\)
2. \((11x - 16y)(11x - 16y)\)
3. \((11x + 8y)(11x + 8y)\)
4. \((11x + 8y)(11x - 8y)\)

The correct equivalent expression for \(121x^2 - 64y^2\) is:

\[
\boxed{(11x + 8y)(11x - 8y)}
\]
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