Question
Factor the expression below.
25x^2-49
0(5x- 7)(5x- 7)
0(5x+7)(5x-7)
0(25X+ 7)(x-7)
0(25x-7)(x- 7)
25x^2-49
0(5x- 7)(5x- 7)
0(5x+7)(5x-7)
0(25X+ 7)(x-7)
0(25x-7)(x- 7)
Answers
Answered by
GPT-4o mini
To factor the expression \( 25x^2 - 49 \), we recognize that it is a difference of squares. The formula for factoring a difference of squares \( a^2 - b^2 \) is given by:
\[
a^2 - b^2 = (a - b)(a + b)
\]
In this case, we can identify \( a = 5x \) (since \( (5x)^2 = 25x^2 \)) and \( b = 7 \) (since \( 7^2 = 49 \)). Thus, we can apply the difference of squares formula as follows:
\[
25x^2 - 49 = (5x - 7)(5x + 7)
\]
So, the correct factorization of the expression \( 25x^2 - 49 \) is:
\[
(5x - 7)(5x + 7)
\]
Among the options you provided, the correct answer is:
\[
0(5x + 7)(5x - 7)
\]
\[
a^2 - b^2 = (a - b)(a + b)
\]
In this case, we can identify \( a = 5x \) (since \( (5x)^2 = 25x^2 \)) and \( b = 7 \) (since \( 7^2 = 49 \)). Thus, we can apply the difference of squares formula as follows:
\[
25x^2 - 49 = (5x - 7)(5x + 7)
\]
So, the correct factorization of the expression \( 25x^2 - 49 \) is:
\[
(5x - 7)(5x + 7)
\]
Among the options you provided, the correct answer is:
\[
0(5x + 7)(5x - 7)
\]
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