8-4 Multiplying Special Cases

Objectives

To find the square of a binomial and to find the product of a sum and difference

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Essential Understanding There are special rules you can use to simplify the square of a binomial or the product of a sum and difference.

Squares of binomials have the form ( a + b ) 2 open eh plus b close squared  or ( a − b ) 2 . open eh minus b close squared . .  You can algebraically simplify the product or you can use an area model to discover the rule for simplifying ( a + b ) 2 , open eh plus b close squared . comma  as shown below.

Simplify the product.

Area Model

( a + b ) 2 = ( a + b ) ( a + b )     = a 2 + a b + b a + b 2 Multiply the binomials .   = a 2 + 2 a b + b 2 Simplify . table with 3 rows and 4 columns , row1 column 1 , open eh plus b close squared , column 2 equals , column 3 open eh plus b close open eh plus b close , column 4 , row2 column 1 , , column 2 equals , column 3 eh squared , plus eh b plus b eh plus , b squared , column 4 cap multiplythebinomials . . , row3 column 1 , , column 2 equals , column 3 eh squared , plus 2 eh b plus , b squared , column 4 cap simplify , . , end table

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