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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)

Respuesta :

kudzordzifrancis

Answer:

[tex]\boxed{d.\:\:\:9(5x+4)(5x-4)}[/tex]

Step-by-step explanation:


The given expression is


[tex]225x^2-144[/tex]


We rewrite to obtain;


[tex]=(15x)^2-12^2[/tex]


Recall that;

[tex]a^2-b^2=(a+b)(a-b)[/tex]


We apply the difference of two squares formula to obtain;


[tex]=(15x+12)(15x-12)[/tex]


We factor further to obtain;


[tex]=3(5x+4)\times3(5x-4)[/tex]


This will give us;

[tex]=9(5x+4)(5x-4)[/tex]

SaniShahbaz

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


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