Question

Which pattern can be used to factor the high-degree polynomial 16x8−49x2?(1 point)
Responses

(a−b)(a+b)=a2−b2
left parenthesis a minus b right parenthesis left parenthesis a plus b right parenthesis equals a squared minus b squared

Neither the difference of squares nor the perfect square trinomial pattern can be used to factor 16x8−49x2.
Neither the difference of squares nor the perfect square trinomial pattern can be used to factor 16 x superscript 8 baseline minus 49 x squared .

(a+b)2=a2+2ab+b2
left parenthesis a plus b right parenthesis squared equals a squared plus 2 a b plus b squared

(a−b)2=a2−2ab+b2

Answer 1

To factor the polynomial \( 16x^8 - 49x^2 \), we can use the difference of squares pattern, which states:

\[
a^2 - b^2 = (a - b)(a + b)
\]

In this case, we can observe that \( 16x^8 \) and \( 49x^2 \) are both perfect squares:

- \( 16x^8 = (4x^4)^2 \)
- \( 49x^2 = (7x)^2 \)

Thus, we can rewrite the polynomial as:

\[
(4x^4)^2 - (7x)^2
\]

Now, applying the difference of squares formula:

\[
(4x^4 - 7x)(4x^4 + 7x)
\]

Therefore, the correct option for the pattern to factor \( 16x^8 - 49x^2 \) is:

\[
(a − b)(a + b) = a^2 − b^2
\]

So the response is:

**(a − b)(a + b) = a^2 − b^2.**