Author: mark_cameron
Last saved by: Glencoe Mathematics
Company: McGraw-Hill

Lesson 12-3

Example 1 Simplify a Polynomial
Simplify –3a + 2b + 5a – 4b.

The like terms in this expression are –3a and 5a, and 2b and –4b.

–3a + 2b + 5a – 4b	Write the polynomial.
	= –3a + 2b + 5a + (–4b)	Definition of subtraction
	= (–3a + 5a) + [2b + (–4b)]	Group like terms.
	= 2a + (–2b) or 2a – 2b	Simplify by combining like terms.

Example 2 Simplify Polynomials
Simplify 3x^2 + 2 – x^2.

Use the definition of subtraction to write this polynomial as 3x^2 + 2 + (–x^2). Then group and add like terms.

3x^2 + 2 + (–x^2)

= [3x^2 + (–x^2)] + 2

= [3x^2 + (–1x^2)] + 2

= 2x^2 + 2

	Example 3 Simplify Polynomials
Simplify x^2 – 2 – 2x + 1 + x.

x^2 + (–2) + (–2x) + 1 + 1x			Write the polynomial.
= x^2 + (–2x + 1x) + (–2 + 1)		Group like terms.
= x^2 + (–1x) + (–1)		Simplify by combining like terms.
= x^2 – x – 1	1x = x