Question

Which pattern can be used to factor the high-degree polynomial 16x8−49x2
16
𝑥
8
−
49
𝑥
2
?(1 point)
Responses

(a+b)2=a2+2ab+b2
(
𝑎
+
𝑏
)
2
=
𝑎
2
+
2
𝑎
𝑏
+
𝑏
2
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
16
𝑥
8
−
49
𝑥
2
.
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)(a+b)=a2−b2
(
𝑎
−
𝑏
)
(
𝑎
+
𝑏
)
=
𝑎
2
−
𝑏
2
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

Answer 1

To factor the polynomial \( 16x^8 - 49x^2 \), you can recognize that it fits the pattern of a difference of squares, which is given by the identity:

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

In your case, you can rewrite the polynomial as follows:

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

Here, \( a = 4x^4 \) and \( b = 7x \), allowing us to apply the difference of squares formula:

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

Therefore, the correct response is:

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

This means the appropriate answer is the one that states the use of the difference of squares pattern, which is:

**(a−b)(a+b)=a2−b2** (the difference of squares).