2-5 HW = Pg. 96-98 #16-60eoe, 76-96 e

2-5 HW Continued

You can use algebra tiles to model algebraic expressions.

11 1-tile

This 1-by-1 square tile has an area of 1 square unit.

x-tile

x

1

This 1-by-x square tile has an area of x square units.

3

x + 2Area = 3(x + 2)

3

2

3

x Area = 3(x ) + 3(2)

Model the Distributive Property using Algebra Tiles

MODELING THE DISTRIBUTIVE PROPERTY

x + 2

+

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.

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 property

to 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

SIMPLIFYING BY COMBINING LIKE TERMS

Each of these terms is the product of a number and a variable.terms

+– 3y2x +– 3y2x

number

+– 3y2x

variable.

+– 3y2x

–1 is the coefficient of x.

3 is the coefficient of y2.

x is the variable.

y is the variable.

Each of these terms is the product of a number and a variable.

x2 x2y3 y3

Like terms have the same variable raised to the same power.

y2 – x2 + 3y3 – 5 + 3 – 3x2 + 4y3 + y

variable power.Like terms

The constant terms –5 and 3 are also like terms.

Combine like terms.

SIMPLIFYING BY COMBINING LIKE TERMS

4x2 + 2 – x2 =

(8 + 3)x Use the distributive property.

= 11x Add coefficients.

8x + 3x =

Group like terms.

Rewrite as addition expression.

Distribute the –2.

Multiply.

Combine like terms and simplify.

4x2 – x2 + 2

= 3x2 + 2

3 – 2(4 + x) = 3 + (–2)(4 + x)

= 3 + [(–2)(4) + (–2)(x)]

= 3 + (–8) + (–2x)

= –5 + (–2x)

= –5 – 2x

More Practice

1.) 5(w-8)

2.) (y+2)7

3.) (12-x)y

4.) -4(u+2)

2 2

2

55.) ( 6)( )

66.) -3y-2x+3x+5y

7.) 3x 4 8 7 2

8.) -6w-12-3w+2w 8

b

x x x

2

2

:

1.) 5w-40

2.) 7y+14

3.) 12y-xy

4.) -4u -8

5 5 55.) (6)( ) 5

6 6 66.) 2y+x

7.) -4x 2 8

8.) -9w-4+2w

Answers

b b

x

When will I ever use

this?

Check Yourself

Pg. 103- 107 #20-68 eoe, 70-74, 94-112 e and Quiz 2 #2-18 study

• # 20-24: rewrite if false to make it true• #26-48: use the distributive property to

rewrite the expression without parentheses• #50-68: simplify by combining like terms• #70-74: real world application problems• #94-112: mixed review