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

Question

Responses

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)(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
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Answer 1

To factor the polynomial \(16x^8 - 49x^2\), we can recognize that it fits the form of a difference of squares. In general, the difference of squares pattern is given by:

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

We can rewrite the polynomial as follows:

1. Identify \(a\) and \(b\):

   • \(a^2 = 16x^8\) implies \(a = 4x^4\) (since \((4x^4)^2 = 16x^8\))
   • \(b^2 = 49x^2\) implies \(b = 7x\) (since \((7x)^2 = 49x^2\))

2. Now we can apply the difference of squares pattern: \[ 16x^8 - 49x^2 = (4x^4)^2 - (7x)^2 = (4x^4 - 7x)(4x^4 + 7x) \]

Thus, the answer to the question is: (a−b)(a+b)=a^2−b^2.