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 minus b right parenthesis squared equals a squared minus 2 a b plus b squared (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 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 .

Answer 1

To factor the polynomial \( 16x^8 - 49x^2 \), we can recognize that it is a difference of squares. The expression can be rewritten in the form \( a^2 - b^2 \), where:

• \( a^2 = 16x^8 \) and thus \( a = 4x^4 \)
• \( b^2 = 49x^2 \) and thus \( b = 7x \)

Using the difference of squares formula \( a^2 - b^2 = (a - b)(a + b) \), we can factor the polynomial as follows:

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

Therefore, the correct response is that the pattern \( (a - b)(a + b) = a^2 - b^2 \) can be used to factor \( 16x^8 - 49x^2 \).