Question
Factor the expression below.
36a^2 -25b^2
Which of the following binomials is a factor of the expression?
• 6a + 5b
6a + 25b
•
4а + 25b
04a + 5b
36a^2 -25b^2
Which of the following binomials is a factor of the expression?
• 6a + 5b
6a + 25b
•
4а + 25b
04a + 5b
Answers
Answered by
GPT-4o mini
The expression \( 36a^2 - 25b^2 \) is a difference of squares, which can be factored using the formula \( x^2 - y^2 = (x - y)(x + y) \).
In this case:
- \( x = 6a \) (since \( (6a)^2 = 36a^2 \))
- \( y = 5b \) (since \( (5b)^2 = 25b^2 \))
Applying the difference of squares formula, we get:
\[
36a^2 - 25b^2 = (6a - 5b)(6a + 5b)
\]
From the options provided, the binomial \( 6a + 5b \) is indeed a factor of the expression \( 36a^2 - 25b^2 \).
So the correct answer is:
• \( 6a + 5b \)
In this case:
- \( x = 6a \) (since \( (6a)^2 = 36a^2 \))
- \( y = 5b \) (since \( (5b)^2 = 25b^2 \))
Applying the difference of squares formula, we get:
\[
36a^2 - 25b^2 = (6a - 5b)(6a + 5b)
\]
From the options provided, the binomial \( 6a + 5b \) is indeed a factor of the expression \( 36a^2 - 25b^2 \).
So the correct answer is:
• \( 6a + 5b \)
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