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

Answer:

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

Step-by-step 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;

$=3(5x+4)\times3(5x-4)$

This will give us;

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

Answer 2

Ans:

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

Step-by-step 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