Explanation Given binomial: The given binomial is 54 -2 x 3 y 3 Definitions /Methodused: A monomial is an expression having single term which is the product of a constant and one or more variable x or y (say) with non-negative powers, e.g. 3 x 2 and 4 x y 3 are the monomials. A binomialis an expression consists of sum of two monomials, e.g. x 2 + x y 2 , x 3 + x y 2 etc. The factors of given binomial of the form a 3 - b 3 can be determined by transforming this expression into a formula as follows: a 3 - b 3 = a 3 - a 2 b + a 2 b + a b 2 - a b 2 - b 3 = ( a 3 - a 2 b ) + ( a 2 b - a b 2 ) + ( a b 2 - b 3 ) ⇒ a 2 ( a - b ) + a b ( a - b ) + b 2 ( a - b ) = ( a - b ) ( a 2 + a b + b 2 ) . Thus, the formula is a 3 - b 3 = ( a - b ) ( a 2 + a b + b 2 ) Calculations: The given binomial can be written as 54 − 2 x 3 y 3 = 2 [ 27 − x 3 y 3 ] = 2 [ ( 3 ) 3 − ( x y ) 3 ]

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ISBN: 9780134650111

Author: Martin-Gay

Publisher: PEARSON

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Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.

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Chapter 13, Problem 37R

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To find:The factors of given binomial 54-2x3y3 .

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Chapter 13, Problem 36R

Chapter 13, Problem 38R

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ALGEBRA FOUNDATIONS PREALG.>NASTA ED.<

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The factors of given binomial 54 -2 x 3 y 3 .

Solution Summary: The author explains that a monomial is an expression having single term which is the product of constant and one or more variable x or y with non-negative powers.

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To find:The factors of given binomial 54-2x3y3 .

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