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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

8. Differences of Squares

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Exercise 39 Page 61

Identify and factor out the greatest common factor (GCF) of the expression.

3(m^4+81)

Practice makes perfect

Let's start by identifying the greatest common factor (GCF) of the given expression. 3m^4+243The greatest common factor (GCF) of an expression is a common factor of the terms in the expression. It is the common factor with the greatest coefficient and the greatest exponent. The GCF of the given expression is 3.

3m^4+243

SplitIntoFactors

Split into factors

3* m^4+ 3* 81

Factor out 3

3(m^4+81)

Now, look closely at the expression m^4+81. Let's notice that we can rewrite it as a sum of two perfect squares.

m^4+81

▼

Write as a power

SplitIntoFactors

Split into factors

m^(2(2))+81

a^(m* n)=(a^m)^n

(m^2)^2+81

Write as a power

(m^2)^2+9^2

A sum of two perfect squares is a prime polynomial and cannot be factored. Therefore, the simplest form of the given expression is 3(m^4+81).

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Exercises p.60-63