Teacher note The Commutative Property is the next

Teacher note: The Commutative Property is the next lesson. Therefore keep combining like terms simple! Cannot write in good form because that requires commutative property. For example 3 + 3 x cannot be rewritten as 3 x + 3 because that would require commutative property.

1 -5 The Distributive Property Algebra 1 Glencoe Mc. Graw-Hill Linda Stamper

The Distributive Property To distribute means to give something to each member of a group. In algebra, the distributive property means to distribute multiplication over addition or subtraction. a(b + c) = ab + ac 8(x + 5) = 8 x + 8 • 5 = 8 x + 40 a(b – c) = ab – ac 8(x – 5) = 8 x – 8 • 5 = 8 x - 40 It does not matter which side of the parentheses the multiplier is on. 8(x + 5) is the same as (x + 5)8

Rewrite using the distributive property. Then simplify. Write the problem. Distribute. Simplify. 3(x + 1) 3 x + 3(1) optional step 3 x + 3 An expression is simplified if it has: no grouping symbols, no like terms, and no double signs.

Note: Good form dictates that a coefficient comes before the variable in the answer. 5 n variable coefficient Therefore, write 5 n in your answer instead of n 5. If n was for notebooks, you would say, “ 5 notebooks”. You would not say, “notebooks 5”.

Rewrite using the distributive property. Then simplify. Example 1 Example 2 5(y – 3) 5 y – 5(3) (x – 1)7 x 7 – 1(7) 5 y – 15 7 x – 7 Example 5 Example 3 2 / / Example 6 Example 4 (y + 2)─3 4 / / y(─3) + 2(─ 3) – 3 y + ─ 6 – 3 y – 6 Example 7 Your answer must be simplified. Undo the double signs.

The Distributive Property The Symmetric Property of Equality allow the Distributive Property to be written as follows. If a(b + c) = ab + ac then ab + ac = a(b + c) If 8(x + 5) = 8 • x + 8 • 5 then 8 • x + 8 • 5 = 8(x + 5) An algebraic expression is easier to evaluate when it is simplified. The distributive property allows you to combine like terms by adding their coefficients. What is a term?

A term is a number or the product of a number and variable/s. one term –– + Terms are separated by addition. two terms

An algebraic expression is easier to evaluate when it is simplified. The distributive property allows you to combine like terms by adding their coefficients. What is a coefficient? In a term that is the product of a number and a variable, the number is called the coefficient of the variable. – 1 is the coefficient of x – 1 x + 3 x 2 3 is the coefficient of x 2

Like terms are terms in an expression that have the same variable raised to the same power. 8 x and 3 x Like Terms 4 x 2 and 4 x 7 m and – 2 m 25 and 10 Not Like Terms Constants are considered like terms.

The problem. Use the Identity Property to name the coefficient. Distribute. Simplify. 4 c – c 4 c – 1 c – – (4 – 1 )c 3 c If you have 4 cookies and you eat a cookie, how many cookies are left? This is the mathematical proof for combining like terms!

Simplify the expression. 2 + 9 n 2 + 10 n 3 n — — (3 + 9)n 2 + 10 n Write problem. Distribute Combine like terms. 12 n 2 + 10 n Like terms are terms in an expression that have the same variable raised to the same power. Copy in your spiral notebook!

Simplify – you must show your support work. Example 8 Example 9 Example 10 Example 11 Example 12 Example 13 Example 14 Example 15 Example 16

Simplify – you must show your support work. Example 8 Example 9 Example 10 Example 11 Example 12 Example 13

Simplify – you must show your support work. Example 14 Example 15 Example 16

1 -A 7 Pages 30 -31 #24 -33, 36 -42, 48 -49, 56 -59.