   Chapter A.4, Problem 16E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

In Exercises 9 to 16, factor each trinomial product. 4 a 2 + 12 a b + 9 b 2

To determine

To factor:

The trinomial 4a2+12ab+9b2

Explanation

Approach:

Factorizing a polynomial is to express the polynomial as a product of simpler expressions such that each of the simpler expressions divides the polynomial completely and also the product of all the simpler expressions gives the polynomial.

Calculation:

Given,

4a2+12ab+9b2

First look for a common factor (GCF) of the terms 4a2, 12ab and 9b2.

But, the GCF is 1.

Now, let us factorize the given expression 4a2+12ab+9b2 by the reverse FOIL method.

First factorize the product of the coefficient of the first tern and the constant, such that the sum of the factors gives the coefficient of the middle term.

Thus, factorize 36b2 as 6b·6b such that the sum of the factors (6b+6b) gives 12b.

Now, split the middle term 12ab as 6ab+6ab

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