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Algebra I: Chapter 1 Section 5 Part 2
WARM UP: Use your knowledge of the distributive property to evaluate
1) The art room has 4x number of brushes, 2y number of colored pencils, and z number of paint cans. By
the end of the week the art teacher wants 4 times as many art supplies.
Write an expression using the distributive property for how many art supplies the teacher will have and
simplify.
4(4x + 2y + z) = 16x + 8y + 4z
2) -4 (4 – x )
-16 + 4x
3) 4(8p + 4q – 7r)
32p + 16q – 28r
4) -2 (-1 - 2y)
2 + 4y
Practice Word Problems:
WORD PROBLEM #1: The X Games last 4 days in Los Angeles, California. There are BMX,
Skateboarding, MOTO, and Rally Car Events. The expected attendance on each day for BMX is 12,000
people, for Skateboarding 15, 000 people and for both MOTO and Rally Car 25,000 people.
Use the distributive property to determine how many people attended the X Games during those 4 days.
One day = 12,000 + 15,000 + 25,000 + 25,000)
4(12,000 + 15,000 + 25,000 + 25,000) = 308,000
WORD PROBLEM #2: In a typical week, the administrative assistance spends 10 hours using email, 12
hours meeting people and 6 hours on the phone.
Set up an expression to determine how many hours the administrative assistant spends on these activities
after 12 weeks of work.
12 (10e + 12m + 6p) = 120e + 144m + 72 p
NOTES:
What is a like term?
Any terms that contain the same variables and the same number of each variable (look at exponents) are called
like terms. Numbers by themselves are like terms together
Identify the Like Terms
7x + 3 – 4yx + 2 – 8x
5x2 + 7 – 4y + 6y – x
3, 2 and 7x, -8x
-4y, 6y
2x - x2 – x + 5
m3 + m2 + m – 5 + 6m2
m2, 6m2
2x, -x
What is a coefficient?
The number value of a term or the number multiplied with the variables.
Identify the Coefficients for each term
7x + 3
7 for x
5x2 + 6y – x
-1 for x, 6 for y, 5 for x2
m + 2n2
1 for m, 2 for n2
What does it mean to combine like terms?
Add or subtract the coefficients of like terms.
Combine Like Terms
15x + 18x + 1
33x + 1
10n + 10n2 + 9n2 - 7
10n + 19n2 - 7
To SIMPLIFY an expression do the Distributive Property AND/ OR THEN Combine Like Terms
Examples:
1) 3 (x + 4) + 2
5) 5(x + 3) + 7 (4 + 2x)
3x + 14
24x + 43
2) 5(y + 2) + 7y
12y + 10
6) –9 ( 5r – 3) + 16
-45r + 43
3) 6(x – 2) – 8
6x - 20
7) – 3 (z + y) – 4 (3 + z)
-7z - 3y - 12
4) x (y – 2) + 2x
xy
Work on Your Own: Simplify the following. You may need a separate sheet of paper
1) x + 3 – 5x + 7 + 4y
6) 5(x –2) + 9(y –x)
-4x + 10 + 4y
-4x – 10 + 9y
2) 2x + 7x2 – 9x + 21x3
-7x + 7x2 + 21x3
7) 3xy + 6x + x (3y - 6)
6xy
3) 5 (2r + 6) – 12r
-2r + 30r
8) 2y + 7 – 3( -6 + 3y)
-7y + 25
4) -7 (3x –4) + 2
-21x + 30
9) 8(2y + 4) –3(3y + 6)
7y + 14
5) x (2y + 7) + y (9 + 5x)
7xy + 7x + 9y
10) 5 (3m – 2n) – m ( -7 + 11n)
22m -10n - 11mn
HOMEWORK: pp. 30 –31 #39 – 41, and 43- 51 (odd)