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Chapter 6: Q 6.46TI. (page 593)

Factor:9y2+24y+16.

Short Answer

Expert verified

Factors of 9y2+24y+16is 3y+42, that is3y+43y+4.

Step by step solution

01

Step 1. Given information.

Given an expression9y2+24y+16.

02

Step 2. Find if first and last term are perfect squares or not.

First term is 9y2which can be expressed as 3y2.

Last term is 16 which can be expressed as 42.

Consider a=3yand b=4.

So, both first and last term are a perfect square.

03

Step 3. Check if the middle term is of the form ±2ab.

Here, middle term is 24ywhich can be expressed as 2脳3y脳4.

It can be seen that middle term is of the form2ab.

04

Step 4. Write the square of the binomial.

So, 9y2+24y+16is a perfect square trinomial of the form .

Note that .

Therefore,9y2+24y+16=3y+42.

05

Step 5. Check by multiplying.

Verification can be obtained as follows.

3y+42=3y2+2脳3y脳4+42=9y2+24y+16

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