Download 1-7 The Distributive Property

Objective: Use the distributive property to
simplify expressions.
A.SSE.1.a: Interpret parts of an expression, such as
terms, factors, and coefficients.
Ex:
Simplify 8(x+5)
Think Area of a Rectangle ( length times width)
8 *(x+5)
(x+5)
8
= 8*(x+5)
x
8
5
= 8(x) + 8(5)
=8x + 40
 DEF: Distributive
Property-
• Let a, b, and c be real numbers.
Algebra
Examples
a(b +c) = ab + bc
4(20 + 6) = 4(20) + 4(6)
(b + c)a= ba + ca
(20+6)4 = 20(4) + 6(4)
a(b – c) = ab – ac
7(30 – 2) = 7(30) – 7(2)
(b – c)a = ba – ca
(30 – 2)7 = 30(7) – 2(7)
 Examples:
 3(x
+ 8)
3(x) + 3(8)
3x + 24
Simplify
 (5b
– 4)(-7)  3(0.4 + 1.1c)
5b(-7) – 4(-7) 3(0.4) + 3(1.1c)
-35b + 28
1.2 + 3.3c
 You Try:
5(x+7)
12(3 – 1/6t)
DEF: Term – number, variable, or the product of a
number or variable
DEF: Constant – a term with no variable
DEF: Coefficient – a numerical factor of a term
6a^2 – 5ab + 3b – 12
Term
Term
Term Term
6a^2 – 5ab + 3b – 12
Coefficient
Coefficient
CoefficientConstant
 DEF: Like Terms
– terms that have the
same variable factors.
Terms
7a and -3a
4x^2 and12x^2
8x and -3x^2
Variable
Factors
a and a
x^2 and x^2
x and x^2
Like
Terms?
yes
yes
no
 Simplified
or not??
• 2(3x – 5 + 4x) is not simplified
• 14x – 10 is simplified
 Simplify
by combining like terms.
8x^2 + 2x^2
(8+2)x^2
10x^2
5x – 3 – 3x+ 6y + 4
5x – 3x + 6y – 3 + 4
2x
+ 6y
+1
2x +6y +1
(rearrange)
(combine, pay attention to signs)
(put it all together