Question

Factor 100x^2 - 16

Answers

GPT-4o mini
To factor the expression \(100x^2 - 16\), we can recognize that it is a difference of squares. The general formula for factoring a difference of squares is:

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

In this case:

- \(a^2 = 100x^2\) so \(a = 10x\)
- \(b^2 = 16\) so \(b = 4\)

Now we can apply the difference of squares formula:

\[
100x^2 - 16 = (10x)^2 - 4^2 = (10x - 4)(10x + 4)
\]

Thus, the factored form of \(100x^2 - 16\) is:

\[
(10x - 4)(10x + 4)
\]

You can also factor out a common factor of 2 if desired:

\[
= 2(5x - 2)(5x + 2)
\]

Both forms \( (10x - 4)(10x + 4) \) and \( 2(5x - 2)(5x + 2) \) are valid factored forms.