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).`

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).`