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 + 3x cannot be rewritten as 3x + 3 because that would require commutative property.

1-5 The Distributive Property Algebra 1 Glencoe McGraw-HillLinda Stamper

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 + ac8(x + 5) = 8x The Distributive Property a(b – c) = ab – ac 8(x – 5) = 8x – 8 5 It does not matter which side of the parentheses the multiplier is on. 8(x + 5) is the same as (x + 5)8 = 8x + 40 = 8x - 40

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

coefficient Note: Good form dictates that a coefficient comes before the variable in the answer. 5n coefficient   variable Therefore, write 5n in your answer instead of n5. If n was for notebooks, you would say, “5 notebooks”. You would not say, “notebooks 5”.

5(y – 3) Example 1 5y – 15 5y  –5(3) Rewrite using the distributive property. Then simplify. (x – 1)7 Example 2 7x – 7 x7x7  – 1(7) Example 3  / / 2 / / 4 6 (y + 2) ─ 3 Example 4 –3y y( ─ 3) –3y  +2( ─ 3) + ─6─6 –  Your answer must be simplified. Undo the double signs. Example 5 Example 6 Example 7

The Symmetric Property of Equality allow the Distributive Property to be written as follows. If a(b + c) = ab + ac If 8(x + 5) = 8 x The Distributive Property then ab + ac = a(b + c) then 8 x = 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?

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

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

Like terms are terms in an expression that have the same variable raised to the same power. 8x and 3xLike Terms 4x 2 and 4xNot Like Terms 25 and 10 Like Terms7m and –2m Like Terms Constants are considered like terms.

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

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

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

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

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

1-A7 Pages #24-33,36-42,48-49,56-59.