Chapter 8: Equations & Chapter 8: Equations & InequalitiesInequalities
8.1 – Simplifying Algebraic 8.1 – Simplifying Algebraic ExpressionsExpressions
Simplify Expressions
Simplify 3(x + 5).
3(x + 5) = 3(x) + 3(5)
= 3x + 15
Distributive Property
Simplify.
“SIMPLIFY”
-Eliminate parentheses
-Combine all like terms
“SIMPLIFY”
-Eliminate parentheses
-Combine all like terms
A. A
B. B
C. C
D. D
A. x + 8
B. x + 12
C. 2x + 6
D. 2x + 12
Simplify 2(x + 6).
Simplify (a + 4)7.
(a + 4)7 = a ● 7 + 4 ● 7
= 7a + 28
Distributive Property
Simplify.
1. A
2. B
3. C
4. D
A. 3a + 27
B. 3a + 18
C. 3a + 9
D. a + 18
Simplify (a + 6)3.
Simplify Expressions (Subtraction)
Simplify (q – 3)9.
(q – 3)9 Distributive Property
Simplify
= (q)9
= 9q – 27
– (3)9
1. A
2. B
3. C
4. D
A. q – 16
B. q – 10
C. 8q – 16
D. 8q – 10
Simplify (q – 2)8.
Simplify –3(z – 7).
Distributive Property
Simplify.
–3(z –7) = –3(z)
= –3z + 21
+ (–3)(–7)
REMEMBER: (-) x (-) = (+)
1. A
2. B
3. C
4. D
A. –2z + 8
B. –2z – 8
C. –2z – 4
D. –2z
Use the Distributive Property to rewrite –2(z – 4).
Identify the terms, like terms, coefficients, and constants in 3x – 5 + 2x – x + 7.
Terms:
Like Terms:
Coefficients:
Constants:
3x, -5, 2x, -x, 7
3x, 2x, -x
3, 2, -1
-5, 7
-5, 7
Simplify 8z + 2z – 5 – 9z + 2.
8z + 2z – 5 – 9z + 2
Locate like terms.
= 8z + 2z – 9z – 5 + 2Commutative Property.
= 1z – 3 Simplify
(combine like terms) = z – 3
1. A
2. B
3. C
4. D
A. –z
B. –z + 2
C. z –1
D. –2z
Simplify 6z + z – 2 – 8z + 2.