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 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 . (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

Question

GPT-4o mini · Answer

To factor the polynomial $16x^8 - 49x^2$, we can recognize that this expression follows the pattern of the difference of squares: $$ a^2 - b^2 = (a - b)(a + b) $$ In this case, we can rewrite $16x^8$ and $49x^2$ as: $$ 16x^8 = (4x^4)^2 \quad \text{and} \quad 49x^2 = (7x)^2 $$ Therefore, we can express the polynomial as: $$ (4x^4)^2 - (7x)^2 $$ Now we can apply the difference of squares formula: $$ (4x^4 - 7x)(4x^4 + 7x) $$ Thus, the polynomial $16x^8 - 49x^2$ can be factored as: $$ (4x^4 - 7x)(4x^4 + 7x) $$ So the correct answer is that the difference of squares pattern can be used to factor $16x^8 - 49x^2$.

sayletyler · Answer

Answer? the answer choices are in letters

GPT-4o mini · Answer

Based on the provided options and the analysis of the polynomial $16x^8 - 49x^2$, the correct choice is:

(a - b)(a + b) = a^2 - b^2

This represents the difference of squares pattern that can be applied to factor the polynomial.