Distributive Property Section 2.6

A term is an Expression separated by addition or subtraction. Example 5 m 2x2 How many terms are in:

the numerical part of the term. The coefficient is the numerical part of the term. Examples 1) 4a 4 2) y2 1 3)

Like Terms are 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.

Which of the following is the simplified form of -4x + 7x ? Answer Now

5a and a are like terms and are like terms The above expression simplifies to:

Simplify 1) 5a + 7a 12a 2) 6.1y - 3.2y 2.9y 3) 4x2y + x2y 5x2y 4) 3m2n + 10mn2 + 7m2n - 4mn2 10m2n + 6mn2

Which of the following is the simplified form of 5x - 4 - 7x + 14 ? Answer Now

Distributive property For example: 3(x+2) You simply multiply the number in front of the parenthesis with each part inside the parenthesis. = 3x + 3(2) = 3x+6 3(x+2)

Examples 1. 5(2x+1) 2. -3(x +5) 3. 2 –3(x + 6) = 5(2x) + 5(1)

Group Practice Try the following on your own 4.) 4 + 6(3 – x)

Group Practice (con’t) 4. 4 + 6(3 - x) = 4+ 6(3) - 6(x) = 4 + 18 - 6x = 22 - 6x 5. -2(x+4)+3 = -2(x) + -2(4)+3 = -2x + -8 +3 = -2x – 5 6. 2(x+ 6 – 3) = 2(x) + 2(6) – 2(3) = 2x + 12 – 6 = 2x + 6

Example #2 3(m - 4) 3 • m - 3 • 4 3m - 12 Example #3 -2(y + 3) -2 • y + (-2) • 3 -2y + (-6) -2y - 6

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 Answer Now

Summary The distributive property is used when ________________________. You would not want to use the distributive property when ________ _____________________________.