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EXAMPLES & SOLUTIONS
Anchor 1
Distributing is the reverse of factoring. It multiplies every number inside of the parenthesis by their factor.
Distributing multiples the number outside the parenthesis by each value inside the parentheses.
Combining factoring and distributing simplifies to evaluate.
FACTORING & DISTRIBUTING
Associating factoring with distributing
FACTORING
expression: 2x + 14 + 18
Factoring
List multiplies divisible by GCF (2)
what number times 2 = 2x (1x) OR 2x/2 = 1x
what number times 2 = 18 (9) OR 18/2 = 9
what number times 2 = 14 (7) OR 14/2 = 7
Factor terms by 2
2 (x + 7 + 9)
DISTRIBUTING
expression: 2 (x + 7 + 9)
Distributing
Multiply the outside numbers times the inside numbers:
(2 * x) + (2 * 7) + (2 * 9)
Final Expression:
2x + 14 + 18
Distributive Expressions
Adding, Subtracting, Dividing and Multiplying Expressions
Addition
if x = -1, evaluate: 2(x + 2 + 8)
1) 2 (x + 10) --combine & add like terms
2) (2 * x) + (2 * 10) --distributive property
3) 2x + 20 --updated (factorized) expression
4) (2 * -1) + 20 --substitute -1 for x
5) -2 + 20 = 18 --addition rule
Subtraction
if x = -1, evaluate: 2(x - 2 - 8)
1) 2 (x - 10) --combine & subtract like terms
2) (2 * x) + (2 * (-10)) --distributive property
3) 2x + (-20) --updated (factorized) expression
4) (2 * -1) - 20 --substitute -1 for x
5) -2 -20 = -22 --subtraction rule
Division
if x = 1, evaluate: 2(x + 2)
3(x+ 1)
1) (2 * x) + (2 * 2)
(3 * x) + (3 * 1)
2) 2x + 4
3) 2(1) + 4
3(1) + 3
4) 2 + 4
5)
--updated (factorized) expression
--distributive property
--subtitute 1 for x
--divide rule
6
6
= 1
--addition rule
3x + 3
3 + 3
Multiplication
FOIL Rule:
Each term in the first expression is multiplied by each term in the second.
if x = -1, evaluate: (2x + 2) (1 + 3)
1) (2x * 1) + (2x * 3) + (2 * 1) + (2 * 3) --distributive property
2) 2x + 6x + 2 + 6 --multiply terms (parenthesis)
2) (2x + 6x) + (2 + 6) --combine like terms
3) 8x + 8 --updated expression
4) 8(-1) + 4 --substitute -1 for x
5) -8 + 4 = 4 --addition rule
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