ObjectiveThe student will be able to:

• Combine like terms to simplify expressions.

• Use the distributive property to simplify expressions.

• Simplify expressions using distributive property and like terms together in the same problem.

Designed by Skip Tyler, Varina High School and Nicole Kessinger, Deep Run High School – edited by Gloria Kent, South Lenoir High School, Nov., 2009.

The Distributive PropertyThe process of using the number on the

outside of the parentheses with each term on the inside of the parentheses.a(b + c) = ab + ac and (b + c) a = ba + caa(b - c) = ab - ac and (b - c) a = ba - ca

Example #15(x + 7)

5 • x + 5 • 75x + 35

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?

1. 3(x + y + z) = 3x + 3y + 3z2. (a + b) c = ac + bc3. 6(3k - 4) = 18k - 244. 5(2 + 3x) = 10 + 3x

Answer Now

A term is a1) number,2) variable, or3) a product / quotient of numbers

and variables.Example

5m2x³

The coefficient isthe number attached and in front of

the variable.Examples

1) 4a 42) y2

1

3) 5x2

7 57

Like Terms are terms with the same variable AND with the same

exponent.

To simplify expressions with like terms, simply combine the like terms by adding the coefficients.

Are these like terms?

1) 13k, 22kYes, 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 ?1. -42. 3x3. -3x4. 4

Answer Now

8x 2 2x2 5a a

The above expression simplifies to:

10x2 6a

8x 2 2x2

5a and a are like termsand are like terms

12a2) 6.1y - 3.2y

2.9y3) 4x2y + x2y

5x2y 4) 3m2n + 10mn2 + 7m2n - 4mn2

10m2n + 6mn2

Simplify1) 5a + 7a

21a + 6b6) 4d + 6a2 - d + 12a2

18a2 + 3d

3y4

y4

7)

3y4

1y4

4y4

1y

y

5) 13a + 8a + 6b

Which of the following is the simplified form of

5x - 4 - 7x + 14 ?

Answer Now

1. -12x + 102. -2x + 103. 2x - 184. 12x – 18

If a triangle has sides 3x - 2, 5 - x and 2x - 5, what is the perimeter of the triangle?

Answer Now

1. 4x - 22. 4x + 23. 5x - 24. 5x - 7

Bonus! Which of the following is the simplified form of a + 3a - 4(9 - a) ?

Answer Now

1. -362. 3a - 363. 8a - 364. 8a + 36