Chapter 8.7, Problem 6STP

For Exercises $1-6,$ choose the correct letter.

What is the factored form of $49x^2-56x+16?$

F. ${(7x-4)}^2$

G. $(7x+4)(7x-4)$

H. ${(7x+4)}^2$

I. ${(7x-8)}^2$

To determine

To select the correct option for the factored form of the expression $\left(49x^2-56x+16\right)$ from four options $A.\left(7x-4\right){}^{2}B.\left(7x+4\right)\left(7x-4\right)C.{\left(7x+4\right)}^{2}D.{\left(7x-8\right)}^2$

Answer to Problem 6STP

The correct option is $A.$

Explanation of Solution

Given information:

Given expression $\left(49x^2-56x+16\right)$

Given$\left(49x^2-56x+16\right)=\left({\left(7x\right)}^2-2\left(7x\right)\left(4\right)+4^2\right)$

As we know that $a^2-2ab+b^2={\left(a-b\right)}^2$

Put $a=7x,b=4$ , we get $\left({\left(7x\right)}^2-2\left(7x\right)\left(4\right)+4^2\right)={\left(7x-4\right)}^2$

Therefore, the factors of the given expression are ${\left(7x-4\right)}^2$ .

Hence, the correct option is $A.$