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Factoring Using the Distributive Property, Summaries of Elementary Mathematics

University of California - Los Angeles (UCLA)Elementary Mathematics

Factor – all numbers and variables in a mathematical expression. • GCF (Greatest Common Factor) – The largest factor that divides two or more numbers.

Typology: Summaries

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11/5/2019
1
Factoring Using the
Distributive Property
Vocabulary
•Factor – all numbers and variables in a
mathematical expression
•GCF (Greatest Common Factor) – The largest factor
that divides two or more numbers
•Distributive Property – multiplying an outside
factor with all factors inside of grouping symbols
•Factoring – the process of separating an equation
into its component parts
pf3
pf4
pf5

Partial preview of the text

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Factoring Using the

Distributive Property

Vocabulary

  • Factor – all numbers and variables in a mathematical expression
  • GCF (Greatest Common Factor) – The largest factor that divides two or more numbers
  • Distributive Property – multiplying an outside factor with all factors inside of grouping symbols
  • Factoring – the process of separating an equation into its component parts
  • Monomial – an algebraic expression with only one term
  • Binomial – an algebraic expression with two terms
  • Trinomial – an algebraic expression with three terms
  • Polynomial – an algebraic expression with two or more terms

Introduction

  • We just reviewed how to use the distributive property. You can also reverse the process and express a polynomial in factored form by using the distributive property.

Reversing the Process

  • Factoring polynomials:
3a + 3b
*find the common factor(s) and
remove it from the problem
*write the factor outside of
parentheses and rewrite the rest as
it was in the original
3(a + b)

Ex. 1: Use the distributive property

to factor 10y

2

+ 15y

y y y y y        15 3 5 10 2 5 2

  • Then, express each term as the product of the GCF and its remaining factors.
  • First, find the greatest common factor for 10y^2 and 15y The GCF is 5y. 10y^2 + 15y = 5y(2y + 3)
  • xy – xz
  • xy – xz x is what they have in common
  • x(y – z)
  • 12xy + 6y break down numbers
  • 2∙ 6 x y + 1∙ 6 y both have a 6 y
  • 6y(x + 1 ) *one is a factor of all values Example 2 Example 3 Ex. 4: DIFFICULT 

21ab

  • 33a

bc

1st: Break each term down into numbers and variables

21∙ ab

–33 ∙ a

bc

2 nd:^ Break down numbers into their factors

3 ∙ 7 ∙ ab

–1 ∙ 3 ∙ 11 ∙ a

bc

3 rd: Break up variables with powers to how many

3 ∙ 7 ∙ a ∙ b ∙ b –1 ∙ 3 ∙11∙ a ∙ a ∙ b ∙ c

Now find common factors and form group of leftovers in each term

3 ∙ a ∙ b( 7 ∙ b –1∙11∙ a ∙ c )

3ab(7b –11ac)