Download Document

Distributive Property
• Objective:
• Use the distributive property to simplify
expressions.
The Distributive Property
• The process of distributing the
number on the outside of the
parentheses to each term on the
inside.
•
a(b + c) = ab + ac
and (b + c) a = ba +
a(b - c) = ab - ac
and (b - c) a = ba -
ca
•
ca
• Example #1
• 5(x + 7)
•5•x+5•7
Example #2
3(m - 4)
3•m-3•4
3m - 12
Example #3
-2(y + 3)
-2 • y + (-2) • 3
-2y + (-6)
-2y - 6
Which statement demonstrates the
distributive property incorrectly?
1. 3(x + y + z) = 3x + 3y +
3z
2. (a + b) c = ac + bc
3. 5(2 + 3x) = 10 + 3x
4. 6(3k - 4) = 18k - 24
Answer Now
A term is a
• 1) number,
• 2) variable, or
• 3) a product / quotient of
numbers and variables.
• Example
•5
•m
2
• 2x
The coefficient is
• the numerical part of the term.
• Examples
• 1) 4a
•4
• 2)
2
y
•1
3)
Like Terms are terms with the
same variable AND exponent.
To simplify expressions with like
terms, simply combine the like
terms.
Are these like terms?
1) 13k, 22k
Yes, the variables are the
same.
2) 5ab, 4ba
Yes, the order of the variables
doesn’t matter.
3
3
3) x y, xy
No, the exponents are on
Which of the following is the simplified form of
-4x + 7x ?
1.
2.
3.
4.
-4
3x
-3x
4
Answer Now
and
5a and a
are like terms
are like terms
The above expression simplifies to:
Simplify
1) 5a + 7a
•
•
•
• 12a
2) 6.1y - 3.2y
• 2.9y
2
2
3) 4x y + x y
• 5x2y
2
2
2
2
4) 3m n + 10mn + 7m n - 4mn
• 10m2n + 6mn2
5) 13a + 8a + 6b
• 21a + 6b
• 6) 4d + 6a2 - d + 12a2
2
• 18a + 3d
7)
y
Which of the following is the simplified form of
5x - 4 - 7x + 14 ?
1.
2.
3.
4.
-12x + 10
-2x + 10
2x - 18
12x – 18
Answer Now
If a triangle has sides 3x - 2, 5 - x and 2x 5, what is the perimeter of the triangle?
1.
2.
3.
4.
4x - 2
4x + 2
5x - 2
5x - 7
Answer Now
Which figure below models the simplification
of - 4x - 5 + 7x + 7 using these tiles?
1.
2.
3.
4.
Answer Now
Bonus! Which of the following is the
simplified form of a + 3a - 4(9 - a) ?
1.
2.
3.
4.
-36
3a - 36
8a - 36
8a + 36
Answer Now
Word Problems
1. Write an algebraic expression for each verbal expression. Then
simplify the expression.
(a) six times the difference of 2a and b, increased by 4b
(b). two times the sum of x squared and y squared, increased by
three times the sum of x squared and y squared
Word Problems
Answer Key
1. Write an algebraic expression for each verbal expression. Then
simplify the expression.
(a) 6(2a - b) + 4b
6(2a) - 6(b) + 4b
12a - 6b + 4b
12a - 2b
(b). 2(x^2 + y^2) + 3(x^2 + y^2)
2x^2 + 2y^2 + 3x^2 + 3y^2
2x^2 + 3x^2 + 2y^2 + 3y^2
5x^2 + 5y^2
Word Problems
1. School supplies Kristen purchased two binders that cost $1.25 each,
two binders that cost $4.75 each, two packages of paper that cost $1.50
per package, four blue pens that cost $1.15 each, and four pencils that
cost $.35 each.
(a) Write an expression to represent the total cost of supplies before tax.
(b) What was the total cost of supplies before tax?
2. Sales: Carrie paid $5.00 each for two bracelets and later sold each for
$15.00. She paid $8.00 each for three bracelets and sold each of them
for $9.00.
(a) Write an expression that represents the profit Carrie made.
(b) Evaluate the expression.
3. Mr. Jones is taking the Drama Club on a field trip to see Mozart's
famous opera Don Giovanni. Tickets cost $39 each, and there are 23
students and 2 teachers going on the field trip. Write and evaluate and
expression using the distributive property to find the group's total ticket
cost.
Word Problems
Answer Key
1. (a) 2(1.25 + 4.75 + 1.50) + 4(1.15 + 0.35)
(b) $21.00
2. (a) 2(15 - 5) + 3(9 - 8)
(b) = 2(10) + 3(1) = 23
3. 39(23 + 2) = 39(23) + 39(2)
= 897 + 78
= 975
The group's total ticket cost is $975