How to Do Operations with Polynomials? (+FREE Worksheet!)

Related Topics

• How to Multiply Monomials
• How to Multiply and Dividing Monomials
• How to Multiply Binomials
• How to Factor Trinomials
• How to Add and Subtract Polynomials

Step-by-step guide to doing Operations with Polynomials

• When multiplying a monomial by a polynomial, use the distributive property.
  \(\color{blue}{a×(b+c)=a×b+a×c}\)
• For adding and subtracting polynomials remember to find and combine like terms.

Operations with Polynomials For education statistics and research National Center for Education Statistics.

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Operations with Polynomials – Example 1:

Multiply. \(4(3x-5)-4x=\)

Solution:

Use the distributive property: \(\color{blue}{a×(b+c)=a×b+a×c}\)

Then: \(4(3x−5)= 12x−20\)

Now, combine like terms: \(12x-4x=8x\)

Then simplify: \(4(3x-5)-4x=12x-20-4x=8x-20\)

Operations with Polynomials – Example 2:

Multiply. \(6x(3x+7)+12x-x^2=\)

Solution:

Use the distributive property: \(\color{blue}{a×(b+c)=a×b+a×c}\)

Then: \(6x(3x+7)=18x^2+42x\)

Now, combine like terms: \(18x^2-x^2=17x^2\), \(42x+12x=54x\)

Then simplify: \(6x(3x+7)+12x-x^2= 18x^2+42x+12x-x^2=17x^2+54x\)

Operations with Polynomials – Example 3:

Multiply. \(5(2x-6)-x^2+4x=\)

Solution:

Use the distributive property: \(\color{blue}{a×(b+c)=a×b+a×c}\)

Then: \(5(2x-6)=10x-30 \)

Now, combine like terms: \( 10x+4x=14x\)

Then simplify: \(5(2x-6)-x^2+4x= 10x-30 -x^2+4x=-x^2+14x-30\)

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Operations with Polynomials – Example 4:

Multiply. \(2x(6x+2)= \)

Solution:

Use the distributive property: \(\color{blue}{a×(b+c)=a×b+a×c}\)

Then: \(2x(6x+2)=12x^2+4x \)

Exercises for Solving Operations with Polynomials

Operations with Polynomials

Find each product.

1. \(\color{blue}{3x^2 (6x – 5)+12x}\)
2. \(\color{ blue }{5x^2 (7x – 2)-x^2}\)
3. \(\color{blue}{– 3 (8x – 3)+5x}\)
4. \(\color{blue}{6x^3 (– 3x + 4)-2x^2}\)
5. \(\color{blue}{9 (6x + 2)+14x+8}\)
6. \(\color{blue}{8 (3x + 7)-x^4}\)

Download Operations with Polynomials Worksheet

1. \(\color{blue}{18x^3 – 15x^2+12x}\)
2. \(\color{ blue }{35x^3 – 11x^2}\)
3. \(\color{blue}{–19x + 9}\)
4. \(\color{blue}{–18x^4 + 24x^3-2x^2}\)
5. \(\color{blue}{68x + 26}\)
6. \(\color{blue}{-x^4+24x + 56}\)

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