Question

What is the completely factored from of 9x2+24x+16

(3x+8)(3x+2)
(3x+4)(3x+4)
(9x+8)(x+2)
(9x+4)(x+4)

Answer 1

(3x+4)(3x+4) is factor of given expression.

B is correct.

Explanation:

We are given an expression
`9x^2+24x+16`

Formula:
`a^2+2ab+b^2=(a+b)^2`

First we write each term as perfect square as formula.

`\Rightarrow 9x^2+24x+16`

`\Rightarrow (3x)^2+2\cdot 3x\cdot 4+4^2`

Using formula , a=3x and b=4

`\therefore (3x)^2+2\cdot 3x\cdot 4+4^2=(3x+4)^2`

Now we write same number two times.

Hence, (3x+4)(3x+4) is factor of given expression.