Adding and Subtracting Polynomials

Adding and Subtracting Polynomials

Learn how to add and subtract polynomials and how to combine like terms and simplify polynomials in this article.

Step by step guide to solve adding and subtracting polynomials

  • Adding polynomials is just a matter of combining like terms, with some order of operations considerations thrown in.
  • Be careful with the minus signs, and don’t confuse addition and multiplication!

Example 1:

Simplify the expressions. \((2x^3-4x^4 )-(2x^4-6x^3 )=\)

Solution:

First use Distributive Property for \(-(2x^4-6x^3 )= -2x^4+6x^3 \)
\((2x^3-4x^4 )-(2x^4-6x^3 )=2x^3-4x^4-2x^4+6x^3 \)
Now combine like terms: \(2x^3-4x^4-2x^4+6x^3=-6x^4+8x^3\)

Example 2:

Add expressions. \((x^3-2)+(5x^3-3x^2 )=\)

Solution:

Remove parentheses: \((x^3-2)+(5x^3-3x^2 )=x^3-2+5x^3-3x^2\)
Now combine like terms: \(x^3-2+5x^3-3x^2=6x^3-3x^2-2\)

Example 3:

Subtract. \((4x^3+3x^4 )-(x^4-5x^3 )=\)

Solution:

First use Distributive Property for \(-(x^4-5x^3 ), → -(x^4-5x^3 )=-x^4+5x^3 \)
\( (4x^3+3x^4 )-(x^4-5x^3 )=4x^3+3x^4-x^4+5x^3 \)
Now combine like terms: \(4x^3+3x^4-x^4+5x^3=2x^4+9x^3\)

Example 4:

Add expressions. \((2x^3-6)+(9x^3-4x^2 )=\)

Solution:

Remove parentheses: \((2x^3-6)+(9x^3-4x^2 )=2x^3-6+9x^3-4x^2\)
Now combine like terms: \(2x^3-6+9x^3-4x^2=11x^3-4x^2-6\)

Exercises

Simplify each expression.

  1. \(\color{blue}{(2x^3 – 2) + (2x^3 + 2)}\)
  2. \(\color{blue}{(4x^3 + 5) – (7 – 2x^3)}\)
  3. \(\color{blue}{(4x^2 + 2x^3) – (2x^3 + 5)}\)
  4. \(\color{blue}{(4x^2 – x) + (3x – 5x^2)}\)
  5. \(\color{blue}{(7x + 9) – (3x + 9)}\)
  6. \(\color{blue}{(4x^4 – 2x) – (6x – 2x^4)}\)

Download Adding and Subtracting Polynomials Worksheet

  1. \(\color{blue}{4x^3 }\)
  2. \(\color{blue}{6x^3 – 2}\)
  3. \(\color{blue}{4x^2 – 5}\)
  4. \(\color{blue}{– x^2 + 2x}\)
  5. \(\color{blue}{4x}\)
  6. \(\color{blue}{6x^4 – 8x}\)

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