Question

Factor the trinomial 16x2−56x+49 16x2−56x+49=(Ax−B)2 where A is and B is .

Answer 1

Given

$16x^2-56x+49$

We rewrite in the form: a² + 2ab + b²

This is:

$\begin{gathered} 16x^2=(4x)^2 \\ 49=7^2 \\ -56x=-2(4x)(7) \end{gathered}$

Substituting we get:

$(4x)^2-2(4x)(7)+7^2$

Apply the square binomial formula:

$(4x-7)^2$

Answer:

A is 4

B is 7