Question

Factoring trinomials and difference of squares. I need to understand the steps.

Answer 1

Answer:

Factoring the term $3x^2-75$ we get $\mathbf{3(x+5)(x-5)}$

Step-by-step explanation:

We need to solve the polynomial: $3x^2-75$

First we see that 3 is common term, so taking 3 as common

$3(x^2-25)$

We know that 25 = 5x5 = 5²

So, replacing 25 with 5²

$3(x^2-5^2)$

We know that, $a^2-b^2=(a-b)(a+b)$

Applying this in our equation: $x^2-5^2=(x+5)(x-5)$

$3(x+5)(x-5)$

So, factoring the term $3x^2-75$ we get $\mathbf{3(x+5)(x-5)}$