2-5 (Part I) Applying the Distributive Property

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2-5 (Part I) Applying the Distributive Property Objective: Students will evaluate algebraic expressions and identify parts of an expression. Standard: A.SSE.1 & A.SSE.2

Equivalent Expression Two expressions that have the same value for all values of the variable. Distributive Property Used to find the product of a number and a sum or difference. a (b + c) = ab + ac

The parts of an expression that are added together. Term The parts of an expression that are added together. Coefficient The number part of a term with a variable part. Ex 2x coefficient Constant Term A number part with NO variable part. Like Terms Terms that have the same variable parts.

Coefficient Constant -4 x + 2x - 7 Terms

Example 1 3(x + 6)= (n + 5)n = y(y – 12) = 3x + 18 n2 + 5n y2 – 12y Use the Distributive Property to write an equivalent expression: (remember : Multiply-Multiply) 3(x + 6)= (n + 5)n = y(y – 12) = 3x + 18 n2 + 5n y2 – 12y

Example 2 (y - 2)(-4) = -5x(4 – x) = -(3y – 9) = -4y + 8 -20x + 5x2 Use the Distributive Property to write an equivalent expression: (y - 2)(-4) = -5x(4 – x) = -(3y – 9) = -4y + 8 -20x + 5x2 -1(3y – 9)= -3y + 9 Question: When you distribute -1, what happens to the signs in the parentheses? Answer: They change to their opposites.

Example 3 Identify the terms, like terms, coefficients and constants. -2x – 8 + 6x + 5 Terms: -2x, -8, 6x, 5 Like Terms: -2x and 6x and – 8 and 5 Coefficients: -2 and 6 Constant Terms: -8 and 5

Homework Section 2-5 (Part I) Page 99 (1 – 27 all)

2-5 Applying the Distributive Property (Part II)

Example 1 4x -3 + 5x - 6 Combine like terms 9x - 9 Simplify the expression 4x -3 + 5x - 6 Combine like terms 9x - 9

Example 2 4(n + 9) – 3(2 + n) Distribute 4n + 36 – 6 – 3n Use the Distributive Property to write an equivalent expression: 4(n + 9) – 3(2 + n) Distribute 4n + 36 – 6 – 3n Combine like terms n + 30

Formulas Perimeter of a Rectangle: Area of a Rectangle: P = 2l + 2w OR add all sides Area of a Rectangle: A = lw

Example 3 Find the area and perimeter of the given rectangle: Perimeter: add all sides 3x + 5 =l P = l + l + w + w P = 3x + 5 + 3x + 5 + 4 + 4 4 =w 4 =w 3x + 5 =l P = 6x + 18

Example 3 Find the area and perimeter of the given rectangle: Perimeter: 2l + 2w P = 2l + 2w 4 =w P = 2(3x + 5) + 2(4) P = 6x + 10 + 8 3x + 5 =l P = 6x + 18

Example 3 – Cont. Find the area and perimeter of the given rectangle: A = lw 4 =w A = (3x + 5)(4) A = 12x + 20 3x + 5 =l

Homework Section 2-5 (Part II) Page 99 28 – 41, 50 - 53