Distributive Property

Objective: Use the distributive property to simplify expressions.

The Distributive PropertyThe 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 + caa(b - c) = ab - ac and (b - c) a = ba - ca

Example #15(x + 7)

5 • x + 5 • 75x + 35

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 + bc3. 5(2 + 3x) = 10 + 3x4. 6(3k - 4) = 18k - 24

Answer Now

A term is a1) number,2) variable, or3) a product / quotient of numbers and variables.

Example5m2x2

The coefficient isthe numerical part of the term.

Examples1) 4a

42) y2

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) x3y, xy3

No, the exponents are on different variables.

Which of the following is the simplified form of -4x + 7x ?

1. -42. 3x3. -3x4. 4

Answer Now

The above expression simplifies to:

5a and a are like terms

and are like terms

12a2) 6.1y - 3.2y

2.9y3) 4x2y + x2y

5x2y 4) 3m2n + 10mn2 + 7m2n - 4mn2

10m2n + 6mn2

Simplify1) 5a + 7a

21a + 6b6) 4d + 6a2 - d + 12a2

18a2 + 3d

7)y

5) 13a + 8a + 6b

Which of the following is the simplified form of 5x - 4 - 7x + 14 ?

Answer Now

1. -12x + 102. -2x + 103. 2x - 184. 12x – 18

If a triangle has sides 3x - 2, 5 - x and 2x - 5, what is the perimeter of the triangle?

Answer Now

1. 4x - 22. 4x + 23. 5x - 24. 5x - 7

Which figure below models the simplification of - 4x - 5 + 7x + 7 using these tiles?

Answer Now

1. 2. 3. 4.

Bonus! Which of the following is the simplified form of a + 3a - 4(9 - a) ?

Answer Now

1. -362. 3a - 363. 8a - 364. 8a + 36

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

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

Answer Key

Word Problems1. 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

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 = 975The group's total ticket cost is $975

Answer Key