Question

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

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

(a−b)(a+b)=a2−b2

Answer 1

To factor the polynomial \( 16x^8 - 49x^2 \), we can recognize that it fits the pattern of the difference of squares. The expression can be rewritten as:

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

This allows us to apply the difference of squares factorization, which states that \( a^2 - b^2 = (a - b)(a + b) \).

Here, let:

- \( a = 4x^4 \)
- \( b = 7x \)

Using the difference of squares formula,
\[
16x^8 - 49x^2 = (4x^4 - 7x)(4x^4 + 7x)
\]

Therefore, the correct pattern that can be used to factor \( 16x^8 - 49x^2 \) is:

**(a−b)(a+b)=a²−b²**

So, the correct response is:
**(a−b)(a+b)=a²−b²**.