Adding and Subtracting Polynomials

Adding Polynomials

Adding polynomials involves combining 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

To subtract polynomials, remember to distribute the – sign into all the terms in the parenthesis.

Example:

Simplify –4x + 7 – (5x – 3)

Solution:

–4x + 7 – (5x – 3)

= –4x + 7 – 5x + 3

= –4x + 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

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Adding and Subtracting Polynomials

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