Question

HELP
Sophia’s work factoring a perfect square trinomial is shown below. She has made several mistakes. Explain Sophia’s mistakes and correct her work using complete sentences.

16x^2 – 40x + 25 = (x + 5)^2

Answer 1

Sophia’s work factoring a perfect square trinomial is $(4x+5)^{2}.$

Step-by-step explanation:

We have,

16$x^2$ – 40x + 25

= $(4x)^2$ - 2(4x)(5) + $5^{2}$

Using the algebraic identity,

$(a+b)^{2}=a^{2}+2ab+b^{2}$

= $(4x)^2$ - 2(4x)(5) + $5^{2}$

$= (4x+5)^{2}$ ≠ ($(x + 5)^2$

Thus, Sophia’s work factoring a perfect square trinomial is $(4x+5)^{2}.$