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Learn how to simplify expressions using the distributive property, understand terms, coefficients, and like terms. Practice examples and word problems to boost your algebra skills!
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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 • 5x + 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
Answer Now Which statement demonstrates the distributive property incorrectly? • 3(x + y + z) = 3x + 3y + 3z • (a + b) c = ac + bc • 5(2 + 3x) = 10 + 3x • 6(3k - 4) = 18k - 24
A term is a • 1) number, • 2) variable, or • 3) a product / quotient of numbers and variables. • Example • 5 • m • 2x2
3) The coefficient is • the numerical part of the term. • Examples • 1) 4a • 4 • 2) y2 • 1
Like Termsare 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.
Answer Now Which of the following is the simplified form of -4x + 7x ? • -4 • 3x • -3x • 4
The above expression simplifies to: are like terms and 5a and a are like terms
Simplify1) 5a + 7a • 12a • 2) 6.1y - 3.2y • 2.9y • 3) 4x2y + x2y • 5x2y • 4) 3m2n + 10mn2 + 7m2n - 4mn2 • 10m2n + 6mn2
7) y 5) 13a + 8a + 6b • 21a + 6b • 6) 4d + 6a2 - d + 12a2 • 18a2 + 3d
Answer Now Which of the following is the simplified form of 5x - 4 - 7x + 14 ? • -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? • 4x - 2 • 4x + 2 • 5x - 2 • 5x - 7
Answer Now Which figure below models the simplification of - 4x - 5 + 7x + 7 using these tiles?
Answer Now Bonus! Which of the following is the simplified form of a + 3a - 4(9 - a) ? • -36 • 3a - 36 • 8a - 36 • 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 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
