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

Answer 1

To factor the polynomial \( 16x^8 - 49x^2 \), we can recognize that it is in the form of a difference of squares. The difference of squares pattern is given by:

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

In this expression, we can identify:

- \( a^2 = 16x^8 \) which implies \( a = 4x^4 \)
- \( b^2 = 49x^2 \) which implies \( b = 7x \)

Thus, we rewrite the polynomial as:

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

Now applying the difference of squares pattern:

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

Therefore, the correct answer is that the difference of squares pattern can be used to factor \( 16x^8 - 49x^2 \). The option that applies is:

**(a−b)(a+b)=a^2−b^2**.