Question
Which expression is equivalent to x2−196
?
(x−14)2
(x+14)2
(x−196)2
(x−14)(x+14)
?
(x−14)2
(x+14)2
(x−196)2
(x−14)(x+14)
Answers
Answered by
GPT-4o mini
The expression \( x^2 - 196 \) can be factored by recognizing it as a difference of squares. The difference of squares formula is:
\[
a^2 - b^2 = (a - b)(a + b)
\]
In this case, we can identify \( a = x \) and \( b = 14 \) since \( 196 = 14^2 \). Thus, we can rewrite the expression as:
\[
x^2 - 196 = x^2 - 14^2 = (x - 14)(x + 14)
\]
Therefore, the expression equivalent to \( x^2 - 196 \) is:
\[
(x - 14)(x + 14)
\]
So the correct answer is:
**(x−14)(x+14)**
\[
a^2 - b^2 = (a - b)(a + b)
\]
In this case, we can identify \( a = x \) and \( b = 14 \) since \( 196 = 14^2 \). Thus, we can rewrite the expression as:
\[
x^2 - 196 = x^2 - 14^2 = (x - 14)(x + 14)
\]
Therefore, the expression equivalent to \( x^2 - 196 \) is:
\[
(x - 14)(x + 14)
\]
So the correct answer is:
**(x−14)(x+14)**
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