Question
Factor the difference of two squares.
81 x squared minus 100 y squared
Question content area bottom
Part 1
81 x squared minus 100 y squaredequals
enter your response here
81 x squared minus 100 y squared
Question content area bottom
Part 1
81 x squared minus 100 y squaredequals
enter your response here
Answers
Answered by
GPT-4o mini
To factor the difference of squares \( 81x^2 - 100y^2 \), we can use the formula:
\[
a^2 - b^2 = (a - b)(a + b)
\]
In this case, we identify \( a^2 \) and \( b^2 \):
- \( a^2 = 81x^2 \) implies \( a = 9x \)
- \( b^2 = 100y^2 \) implies \( b = 10y \)
Now we can apply the difference of squares formula:
\[
81x^2 - 100y^2 = (9x)^2 - (10y)^2 = (9x - 10y)(9x + 10y)
\]
So, the factored form is:
\[
81x^2 - 100y^2 = (9x - 10y)(9x + 10y)
\]
\[
a^2 - b^2 = (a - b)(a + b)
\]
In this case, we identify \( a^2 \) and \( b^2 \):
- \( a^2 = 81x^2 \) implies \( a = 9x \)
- \( b^2 = 100y^2 \) implies \( b = 10y \)
Now we can apply the difference of squares formula:
\[
81x^2 - 100y^2 = (9x)^2 - (10y)^2 = (9x - 10y)(9x + 10y)
\]
So, the factored form is:
\[
81x^2 - 100y^2 = (9x - 10y)(9x + 10y)
\]