Question

What is the expression in factored form?

225x^2 - 144

a. 9(5x+4)^2
b. 9(5x-4)^2
c. 9(4x+5)(4x-5)
d. 9(5x+4)(5x-4)

Answer 1

Ans:

Option d. 9(5x+4)(5x-4)

Explanation:

We are given an expression 225x² - 144 and we have to write it in factored form

225x² - 144

taking 9 common in the above expression

9(25x² - 16)

25x² can be written as (5x)² and 16 as 4²

9((5x)² - 4²)

(5x)² - 4² = (5x+4)(5x-4)

using formula a² - b² = (a+b)(a-b)

9(5x+4)(5x-4) is the solution

Answer 2

`\boxed{d.\:\:\:9(5x+4)(5x-4)}`

Explanation:

The given expression is

`225x^2-144`

We rewrite to obtain;

`=(15x)^2-12^2`

Recall that;

`a^2-b^2=(a+b)(a-b)`

We apply the difference of two squares formula to obtain;

`=(15x+12)(15x-12)`

We factor further to obtain;

`=3(5x+4)*3(5x-4)`

This will give us;

`=9(5x+4)(5x-4)`