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

(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 .

Answer 1

To factor the polynomial \( 16x^8 - 49x^2 \), we can recognize that it fits the difference of squares pattern, which is used for expressions of the form \( a^2 - b^2 = (a - b)(a + b) \).

1. Identify \( a \) and \( b \):
- \( 16x^8 \) can be written as \( (4x^4)^2 \).
- \( 49x^2 \) can be written as \( (7x)^2 \).

2. Apply the difference of squares:
\[
16x^8 - 49x^2 = (4x^4)^2 - (7x)^2 = (4x^4 - 7x)(4x^4 + 7x)
\]

Therefore, the correct pattern to apply here is:
\[
(a - b)(a + b) = a^2 - b^2
\]

So, the response is:
\((a−b)(a+b)=a^2−b^2\) (the difference of squares pattern).