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)

Step-by-step explanation:

The given expression is

We rewrite to obtain;

Recall that;

We apply the difference of two squares formula to obtain;

We factor further to obtain;

This will give us;

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

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for