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# Simplifying Expressions

Overview
• Section 1.8 in the textbook
– Like Terms & Combining Like Terms
– Simplifying Expressions

Like Terms & Combining Like
Terms

Combining Like Terms
• Two terms are said to be like terms if they
satisfy BOTH of the following conditions:
– The variables must be the same
– The variables must be raised to the same
power
(numbers) and retain the variable

Ex 1: Simplify by combining the like terms:

a) 2x + 7 – 5 + x – 1
b) 5a – 2b + 2 – 6b – 3
c) mn + 4m – mn – 2n + m + 9n
d) -x2 + 4x – 3 + 2x2 – x

Simplifying Expressions

• Recall the Distributive Property:
a(b + c) = a · b + a · c
• Usually no operation next to the number
outside of the parentheses
– Implied to be multiplication
• To simplify an expression:
– Apply the Distributive Property if necessary
– Combine any like terms

Ex 2: Simplify:

a) 4(2x – 5) + 3(x + 1)
b) 8(2 – y) – (3 – y)
c) 5(2x2 – 5x + 1) – 3(x3 + x2 – 2) + 2x

Ex 3: Translate and simplify:

a) The difference of (5x – 9) and (x + 2)
b) (9y2 – 5) less (2y2 + y – 3)
c) Subtract (18 – 7z) from (z + 7)

Summary
• After studying these slides, you should
know how to do the following:
– Identify and combine like terms
– Simplify expressions