Section 1.5 Distributive Property

The students will be able to use the distributive property to simplify expressions.

The Distributive PropertyThe process of distributing the number

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

a(b - c) = ab - ac and (b - c) a = ba - ca

Example #1

5(x + 7)

5 • x + 5 • 7

5x + 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 + 3z

2. (a + b) c = ac + bc

3. 5(2 + 3x) = 10 + 3x

4. 6(3k - 4) = 18k - 24

Answer Now

A term is a1) number,

2) variable, or

3) a product / quotient of numbers and variables.

Example

5

m

2x2

The coefficient isthe numerical part of the term.

Examples

1) 4a

4

2) y2

1

3) 5x2

7 5

7

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 ?1. -4

2. 3x

3. -3x

4. 4

Answer Now

8x 2 2x2 5a a

The above expression simplifies to:

10x2 6a

8x 2 2x2

5a and a are like terms

and are like terms

12a

2) 6.1y - 3.2y

2.9y

3) 4x2y + x2y

5x2y

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

10m2n + 6mn2

Simplify1) 5a + 7a

21a + 6b

6) 4d + 6a2 - d + 12a2

18a2 + 3d

3y

4

y

47)

3y

4

1y

4

4y

41y

y

5) 13a + 8a + 6b

Which of the following is the simplified form of

5x - 4 - 7x + 14 ?

Answer Now

1. -12x + 10

2. -2x + 10

3. 2x - 18

4. 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 - 2

2. 4x + 2

3. 5x - 2

4. 5x - 7

Which figure below models the simplification of - 4x - 5 + 7x + 7 using these tiles?

Answer Now

1.

2.

3.

4.

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

Answer Now

1. -36

2. 3a - 36

3. 8a - 36

4. 8a + 36