Distributive Property

• Section 2.5• Page 96

Vocabulary

• Coefficient (of a variable)2x, 5ab, x think (1)x, -y think (-1)y

• Like termsterms that have the same variable raised to the same power. 3x and -8x are like terms

5xy2 and xy2 are like terms• Constant terms - plain numbers – no

variable attached. 3x +7, 5y – 5x - 9

Vocabulary

• Equivalent Expressions– Two expressions that have the same value for all

values of the variable– 2(x + 5) = -2x + -10 both sides are equal

• Distributive Property

Before we discuss the distributive property and how to use it, let’s talk about terms.

Terms are defined by addition signs – how they are separated in an expression

For example: 2y + 3 has two terms, 2y and 3 -6xy has only one term, -6xy has 3 terms, 5x^2, -4x, -725 4 7x x

THE DISTRIBUTIVE PROPERTY

a(b + c) = ab + ac

(b + c)a = ba + ca

2(x + 5) 2(x) + 2(5) 2x + 10

(x + 5)2 (x)2 + (5)2 2x + 10

(1 + 5x)2 (1)2 + (5x)2 2 + 10x

y(1 – y) y(1) – y(y) y – y 2

USING THE DISTRIBUTIVE PROPERTY

=

=

=

=

=

=

=

=

The product of a and (b + c):

(y – 5)(–2) = (y)(–2) + (–5)(–2)

= –2y + 10

–(7 – 3x) = (–1)(7) + (–1)(–3x)

= –7 + 3x

= –3 – 3x

(–3)(1 + x) = (–3)(1) + (–3)(x)

Simplify.

Distribute the –3.

Simplify.

Distribute the –2. Simplify.

–a = –1 • a

USING THE DISTRIBUTIVE PROPERTY

Remember that a factor must multiply each term of an expression.

Forgetting to distribute the negative sign when multiplying by a negative factor is a common error.

Find the difference mentally.

Find the products mentally.

You are shopping for CDs.You want to buy six CDs

for $11.95 each.

Use the distributive propertyto calculate the total cost

mentally.

6(11.95) = 6(12 – 0.05)

Use the distributive property.= 6(12) – 6(0.05)

= 72 – 0.30

= 71.70

MENTAL MATH CALCULATIONS

Find the difference mentally.

Find the products mentally.

The mental math is easier if you think of $11.95 as $12.00 – $.05.

Write 11.95 as a difference.

You are shopping for CDs.You want to buy six CDs

for $11.95 each.

Use the distributive propertyto calculate the total cost

mentally.

6(11.95) = 6(12 – 0.05)

Use the distributive property.= 6(12) – 6(0.05)

= 72 – 0.30

= 71.70

The total cost of 6 CDs at $11.95 each is $71.70.

MENTAL MATH CALCULATIONS

SOLUTION

• You want to buy 4 tires for $44.98 each. Use the distributive property to calculate the total cost mentally.

• The Drama Club is selling candy bars for $1.20 each. You buy seven. Use the distributive property to calculate the total mentally.

• Simplify:• (-x + 9)(3) y ( 2y + 3)

• -4x(2x – 3) 3x(x2 + 5x)

• -2r (-r – 7)

• Assignment: P. 99 (#1-20, 43-44)

• Copy the problem in 5-20, show steps

Make sure you show the distributive property in 43-44 from start to finish!