Page 96 - Algebra 1

Use the Multiplication Property of -1 to simplify an expression like -(5 + 2). Rewrite the expression as -1(5 + 2) and then distribute.
Distributing a Negative Integer
Example
2
Simplify each expression. a. -(9+4)
SOLUTION
-(9 + 4)
= (-1)(9) + (-1)(4) = -9 - 4
= -13
Distribute. Multiply. Simplify.
b. -9(-6-3) SOLUTION
-9(-6 - 3)
= (-9)(-6) + (-9)(-3) = 54 + 27
= 81
Hint
The product of a real number and 1 is the real number.
The Distributive Property of Equality applies not only to numeric expressions but also to algebraic expressions.
Simplifying Algebraic Expressions
Example
3
Simplify each expression. a. -4(x+7)
SOLUTION
-4(x + 7)
= (-4)(x) + (-4)(7) = -4x - 28
Distribute. Multiply.
b. (5-x)6 SOLUTION
(5 - x)6
= 6(5) + 6(-x) = 30 - 6x
Reading Math
There are different ways to write the same expression:
6 · (5 - x) (5 - x) · 6 6(5 - x) (5 - x)6
Example
4
Simplify each expression. a. mn(mx + ny + 2p)
SOLUTION
mn(mx + ny + 2p)
= m2nx + mn2y + 2mnp
b. -xy(y2 - x2z) SOLUTION
−xy(y2 - x2z)
= (-xy)(y2) + (-xy)(-x2z) = -xy3 + x3yz
Multiply.
Distribute.
Combine like terms.
Simplifying Algebraic Expressions with Exponents
Hint
When multiplying, add the exponents of powers with the same base.
y(y2) = y1+2 = y3
Lesson 15 81