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Chapter 6: Q 6.49TI. (page 595)

Factor:49x2+84xy+36y2.

Short Answer

Expert verified

Factors of49x2+84xy+36y2is7x+6y2.

Step by step solution

01

Step 1. Given information.

Given an expression49x2+84xy+36y2.

02

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

First term is 49x2which can be expressed as 7x2.

Last term is 36y2which can be expressed as 6y2.

Consider a=7xand b=6y.

So, first and last term are perfect squares.

03

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

Here, middle term is 84xywhich can be expressed as 2脳7x脳6y.

It follows that middle term is of the form 2ab.

04

Step 4. Write the square of the binomial.

So, 49x2+84xy+36y2is a perfect square trinomial of the form a2+2ab+b2.

Note that a+b2=a2+2ab+b2.

Therefore, 49x2+84xy+36y2=7x+6y2.

05

Step 5. Check by multiplying.

Verification can be obtained as follows.

7x+6y2=7x2+2脳7x脳6y+6y2=49x2+84xy+36y2

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