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