# Distributive Property Objective Use the distributive property to

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 + ca a(b - c) = ab - ac and (b - c) a = ba - ca Example #1 5(x + 7) 5 • x+5 • 7 5 x + 35

Example #2 3(m - 4) 3 • m-3 • 4 3 m - 12 Example #3 -2(y + 3) -2 • y + (-2) • 3 -2 y + (-6) -2 y - 6

Which statement demonstrates the distributive property incorrectly? 1. 3(x + y + z) = 3 x + 3 y + 3 z 2. (a + b) c = ac + bc 3. 5(2 + 3 x) = 10 + 3 x 4. 6(3 k - 4) = 18 k - 24 Answer Now

A term is a 1) number, 2) variable, or 3) a product / quotient of numbers and variables. Example 5 m 2 2 x

The coefficient is the numerical part of the term. Examples 1) 4 a 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) 13 k, 22 k Yes, the variables are the same. 2) 5 ab, 4 ba 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 -4 x + 7 x ? 1. 2. 3. 4. -4 3 x -3 x 4 Answer Now

and 5 a and a are like terms The above expression simplifies to:

Simplify 1) 5 a + 7 a 12 a 2) 6. 1 y - 3. 2 y 2. 9 y 3) 2 4 x y + 2 xy 5 x 2 y 2 2 4) 3 m n + 10 mn + 7 m n - 4 mn 10 m 2 n + 6 mn 2

5) 13 a + 8 a + 6 b 21 a + 6 b 6) 4 d + 6 a 2 - d + 12 a 2 2 18 a + 3 d 7) y

Which of the following is the simplified form of 5 x - 4 - 7 x + 14 ? 1. 2. 3. 4. -12 x + 10 -2 x + 10 2 x - 18 12 x – 18 Answer Now

If a triangle has sides 3 x - 2, 5 - x and 2 x 5, what is the perimeter of the triangle? 1. 2. 3. 4. 4 x - 2 4 x + 2 5 x - 7 Answer Now

Which figure below models the simplification of - 4 x - 5 + 7 x + 7 using these tiles? 1. 2. 3. 4. Answer Now

Bonus! Which of the following is the simplified form of a + 3 a - 4(9 - a) ? 1. 2. 3. 4. -36 3 a - 36 8 a + 36 Answer Now

Word Problems 1. Write an algebraic expression for each verbal expression. Then simplify the expression. (a) six times the difference of 2 a and b, increased by 4 b (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(2 a - b) + 4 b 6(2 a) - 6(b) + 4 b 12 a - 6 b + 4 b 12 a - 2 b (b). 2(x^2 + y^2) + 3(x^2 + y^2) 2 x^2 + 2 y^2 + 3 x^2 + 3 y^2 2 x^2 + 3 x^2 + 2 y^2 + 3 y^2 5 x^2 + 5 y^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

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