# Essential Question: Describe an everyday situation in which the distributive property and mental math would be helpful.

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Essential Question: Describe an everyday situation in which the distributive property and mental math would be helpful.

2-4: The Distributive Property Distributive Property For every real number a, b, and c, a(b + c) = ab + ac(b + c)a = ba + ca a(b – c) = ab – ac(b – c)a = ba – ca I N E NGLISH : If a number is outside parenthesis, you can multiply it to all terms inside the parenthesis Examples: 5(20 + 6) = 5(20) + 5(6) (30 – 2)9 = 30(9) – 2(9)

2-4: The Distributive Property You can use the distributive property to multiply some numbers using mental math instead of a calculator. Example 1: Use the distributive property to simplify 34(102) 102 is simply 100 + 2 34(100 + 2) = 34(100) + 34(2) = 3400 + 68 = 3468

2-4: The Distributive Property Y OUR T URN – S IMPLIFY ( AND TRY TO NOT USE A CALCULATOR ) 13(103) 21(101) 24(98) 15(99) 1339 2121 2352 1485

2-4: The Distributive Property Most of the time, you’ll use the distributive property as a means to simplify algebraic expressions. Example 2: Simplifying an expression 2(5x + 3) = 2(5x) + 2(3) = 10x + 6 Y OUR T URN – S IMPLIFY 2(3 – 7t) (0.4 + 1.1c)3 6 – 14t 1.2 + 3.3c

2-4: The Distributive Property If you see a negative sign in front of parenthesis, you can rewrite using the multiplication property of -1 Example 3: Negative sign in front -(6x + 4) = (-1)(6x + 4) = (-1)(6x) + (-1)(4) = -6x – 4 Y OUR T URN – S IMPLIFY -(2x + 1) (3 – 8a)(-1) -2x – 1 -3 + 8a

2-4: The Distributive Property Term: A number, variable, or the product of a number and one or more variables Constant: A term that has no variable Coefficient: The number part of a term 6a 2 – 5ab + 3b – 12 Like Terms: Have the exact same variable parts Like TermsNot like terms 3x and -2x8x and 7y -5x 2 and 9x 2 5y and 2y 2 xy and –xy4y and 5xy -7x 2 y 3 and 15x 2 y 3 x 2 y and xy 2 Constant Coefficients

2-4: The Distributive Property An algebra expression is in simplest form has no like terms. You use the Distributive Property to combine like terms. Think of the Distributive Property as ba + ca = (b + c)a Example 4: Combining Like Terms 3x 2 + 5x 2 = (3 + 5)x 2 = 8x 2 Y OUR T URN – S IMPLIFY EACH EXPRESSION 7y + 6y 3t – t -9w 3 – 3w 3 8d + d 13y 2t -12w 3 9d

2-4: The Distributive Property The word “quantity” indicates that two or more terms are within parenthesis. Example 5: Writing an expression Write “3 times the quantity x minus 5” 3(x – 5) Your Turn Write “-2 times the quantity t plus 7” -2(t + 7) Write “the product of 14 and the quantity 8 plus w” 14(8 + w)

Assignment Worksheet 2-4 Problems 1 – 53, odds

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