Adding And Subtracting Polynomials

What is a Polynomial?
A polynomial is an expression consisting of variables and coefficients, involving only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables. Like terms are terms that have the exact same variables raised to the same powers.

The following diagram shows examples of adding and subtracting polynomials. Scroll down the page for more examples and solutions on how to add and subtract polynomials.

 

• Printable Polynomial Worksheets

  Add & Subtract Polynomials
  Multiply Polynomials
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Adding Polynomials

To add polynomials, you essentially remove the parentheses (if any) and then combine all the like terms.

Example:
Add the polynomials 5x – 2 + y and –3y + 5x + 2

Solution:
5x – 2 + y + (–3y + 5x + 2)
= 5x + 5x + y – 3y – 2 + 2
= 10x – 2y

Example:
Find the sum of –7x³y + 4x²y² – 2 and 4x³y + 1 – 8x²y²

Solution:
–7x³y + 4x²y²– 2 + 4x³y + 1 – 8x²y²
= –7x³y + 4x³y + 4x²y²– 8x²y² – 2 + 1
= –3x³y – 4x²y² – 1

Subtracting Polynomials

Subtracting polynomials is slightly trickier because of the negative sign. When you subtract a polynomial, you must subtract every term in the second polynomial. This is equivalent to distributing a -1 to every term inside the parentheses being subtracted.

Example:
Simplify –4x + 7 – (5x – 3)

Solution:
–4x + 7 – (5x – 3)
= –4x + 7 – 5x + 3
= –9x + 10

Example:
Simplify (5x² + 2) – (– 4x² + 7) + (– 3x² – 5)

Solution:
(5x² + 2) – (– 4x² + 7) + (– 3x²– 5)
= 5x² + 2 + 4x²– 7 – 3x²– 5
= 5x² + 4x²– 3x² + 2 – 7 – 5
= 6x² – 10

How To Add And Subtract Polynomials?

To add polynomials

1. Combine like terms.
2. Write in descending order.

Examples:

1. (4x² + 8x - 7) + (2x² - 5x - 12)
2. (5 + 24y³ - 7y²) + (-6y³ + 7y² + 5)
3. (t² - t + 5) + (7t² - 4t - 20)

To subtract polynomials

1. Rewrite the subtraction as addition.

To change subtraction to addition, we must add the opposite, or additive inverse. 2. Combine like terms. 3. Write in descending order.

Examples:

1. (4x² + 8x - 7) - (2x² - 5x - 12)
2. (6x⁴ + 3x³ - 1) - (4x³ - 5x + 9)
3. (1.5y³ + 4.8y² + 12) - (y³ - 1.7y² + 2y)

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Examples Of Adding And Subtracting Polynomials

Examples:

1. (2x⁵ - 6x³ - 12x² - 4) + (-11x⁵ + 8x + 2x² + 6)
2. (-9y³ - 6y² - 11x + 2) - (-9y⁴ - 8y³ + 4x² + 2x)

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Adding And Subtracting Polynomials

Adding polynomials and subtracting polynomials is essentially combining like terms of polynomial expressions. When adding and subtracting polynomials, they can either be arranged vertically or grouped according to degree. A knowledge of polynomial vocabulary is important before adding and subtracting polynomials. Multiplying monomials and binomials is another type of operation with polynomials.

Examples:

1. (4x² - 3x + 2) + (5x² + 2x - 7)
2. (5x³ + 7x² - x) + (8x³ + 4x - 5)
3. (8x² + 2x) - (10x² + 2x - 9)
4. -(6x³ - 4x) - (2x³ + x² -2x)

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Adding And Subtracting Polynomials

Examples:

1. (x² + 4x + 5) + (6x + 3)
2. 2(x⁴ + 5x) - 6(x⁴ + 8x - 3)

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