Download Algebra 1 Lesson Notes 2.5

Algebra 1
Lesson Notes 2.5A
Date ________________
Objective: Apply the distributive property.
equivalent expressions: two expressions that have the same value for all values of the
variable.
Distributive Property:
For real numbers a, b, and c,
a(b + c) = ab + ac
(b + c)a= ba + ca
a(b – c) = ab – ac
(b – c)a = ba – ca
A factor outside the parentheses must multiply each term in the parentheses.
Example 1 (p 96): Apply the distributive property
Use the distributive property to write an equivalent expression.
a.
3(x + 6)
b.
(n + 5)n
c.
y(x + y – 12)
d.
(8 – x)9
Example 2 (p 97): Distribute a negative number
a.
(y – 2)(– 4)
b.
− 5x(4 − x)
c.
− (3y − 9)
d.
(3c – 8)(– 5)
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Challenge Example: Distributive property in reverse! This is called factoring.
a.
− 20a + 5b = ____(− 4a + b)
b.
4c – 10d = ____( ___c – ___d)
c.
− 36x2 – 24x = ______(9x + 6)
d.
18xy2 – 8x2y = _______( 9____ − 4x____)
 HW
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A4 pp 99-101 #2-20 even, 56-67
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Algebra 1
Lesson Notes 2.5B
Date ________________
Objective: Combine like terms.
terms: the parts of an expression that are combined (added and subtracted)
coefficient: the number part of a term with a variable
constant or constant term: a term with a number but no variable part
like terms: terms that have exactly the same variable parts; constant terms are like terms
because they all have
no variable
3 terms
 x  3x 12
coefficients are –1 and 3
12 is a constant
− x and 3x are like terms
Example 3 (p 97): Identify parts of an expression
Identify the terms, like terms, coefficients, and constant terms of the expression:
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a.
2 x  8  6 x  5
b.
2  y  8  6y 1
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Combining like terms: the process of combining terms that have the same variable parts.
The distributive property (in reverse) lets you combine like terms that have variables.
(Addition and subtraction let you combine the constants!)
2 x  8  6 x  5
like terms are −2x and 6x, so −2x + 6x = (−2 + 6)x = 4x
−8 and 5 are also like terms, so −8 + 5 = −3
 To combine like terms, combine (add or subtract) the coefficients of the like terms
but DO NOT CHANGE the variable parts!!!!
Simplified expression: an expression is simplified if it has no grouping symbols and all of the
like terms have been combined.
From above:
2 x  8  6 x  5 = 4x − 3
 simplified expression
NOTE: To simplify an expression, FIRST use the distributive property to eliminate any
grouping symbols, THEN combine like terms.
Example 4 (p 98): Simplifying an expression
Which expression is equivalent to 6(x + 3) – 2(8 + x)?
a. 4x + 2
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b. 4x + 34
c. 8x + 2
d. 8x + 34
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Example 5 (p 98): Solve a multi-step problem
Ms. Jenkins rented a rototiller from a garden shop. The rental charge is $28 per day for
the first two days and then $15 per day for each additional day.
a.
Write an equation for t, the total charge, as a function of d, the number of days she
rents the rototiller.
b.
If Ms. Jenkins kept the rototiller for 13 days, what was the total rental charge?
 HW
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A5 pp 99-101 #21-27, 29-41 odd, 47-48, 50-52
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