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 plus b right parenthesis squared equals a squared plus 2 a b plus 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.
1 answer
To factor the polynomial \(16x^8 - 49x^2\), we can recognize it as a difference of squares.
The expression can be rewritten as:
\[ (4x^4)^2 - (7x)^2 \]
This fits the pattern of the difference of squares \(a^2 - b^2 = (a - b)(a + b)\).
Here, \(a = 4x^4\) and \(b = 7x\).
Applying the difference of squares pattern:
\[ 16x^8 - 49x^2 = (4x^4 - 7x)(4x^4 + 7x) \]
Thus, the correct response is:
\((a - b)(a + b) = a^2 - b^2\) (the difference of squares pattern).
