Question
Factor 100x^2 - 16
Answers
Answered by
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.
\[
a^2 - b^2 = (a - b)(a + b)
\]
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.
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