Page 93 - Math Course 2 (Book 1)

Polynomials: Subtraction

Mo. 3

Lesson 6

Subtract Using Additive Inverse
KEY CONCEPTS:
1. Subtracting polynomials.
Examples

MO. 3 - L6a Find (4x – 8) – (3x + 9).

The additive inverse of 3x + 9 is (–1)(3x + 9)
Subtracting Polynomials or –3x – 9.

(4x – 8) – (3x + 9)
= (4x – 8) + (–3x – 9) To subtract (3x + 9), add
Let’s Begin (–3x – 9).

= (4x – 3x) + (–8 – 9) Group the like terms.

Subtract Polynomials = x – 17 Simplify.

Answer The difference is x – 17.
Examples

Find (7a + 4) – (9a + 2). Find (7ab + 2b ) – (3a + ab + b ).
2
2
2
2
7a + 4 The additive inverse of 3a + ab + b is
2
2
2
2
2
(–) 9a + 2 Align like terms. (–1)(3a + ab + b ) or –3a – ab –b .
–2a + 2 Subtract.
Align the like terms and add the additive inverse.
Answer The difference is –2a + 2. 7ab + 2b 2 7ab + 2b 2
2
2
(–) 3a + ab + b 2 (+) –3a – ab – b 2
2
–3a + 6ab – b 2
2
2
Find (8b + 6) – (3b + 6b + 1).
2
8b + 6 Answer The difference is
2
2
–3a + 6ab + b .
2
(–)3b + 6b + 1 Align like terms.
2
5b – 6b + 5 Subtract.
how much more = Nguyen’s allowance – Susan’s
2
Answer The difference is 5b – 6b + 5. allowance
= (2x + 5) – (x + 6) Substitution
Real World Example = (2x + 5) + (–x – 6) Add the additive
inverse.
ALLOWANCE = [2x + (–x)] + [5 + (–6)] Group like terms.
Nguyen receives a monthly allowance from his
parents of 2x + 5. Susan receives an allowance of = x + (–1) or x –1 Simplify.
x + 6. For both, x represents the number of chores
each completed. When x > 2, Nguyen earns more When x > 2, Nguyen earns x – 1
than Susan; how much more does he earn? Answer
dollars more than Susan.

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