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

Do you want to know how to solve Operations with Polynomials? you can do it in one easy steps.

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

Related Topics

Step by step guide to do 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 – 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: \(5(2x-6)-x^2+4x= 10x-30 -x^2+4x=-x^2+14x-30\)

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

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. \(\color{blue}{-x^4+24x + 56}\)

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

How to Determine Limits Using Algebraic Manipulation?How to Determine Limits Using Algebraic Manipulation?
How to Estimate Limit Values from the Graph?How to Estimate Limit Values from the Graph?
Properties of LimitsProperties of Limits
How to Find the Expected Value of a Random Variable?How to Find the Expected Value of a Random Variable?
How to Define Limits Analytically Using Correct Notation?How to Define Limits Analytically Using Correct Notation?
How to Solve Multiplication Rule for Probabilities?How to Solve Multiplication Rule for Probabilities?
How to Solve Venn Diagrams and the Addition Rule?How to Solve Venn Diagrams and the Addition Rule?
How to Find the Direction of Vectors?How to Find the Direction of Vectors?
Vectors IntroductionVectors Introduction
How to Find Addition and Subtraction of Vectors?How to Find Addition and Subtraction of Vectors?

What people say about "How to Do Operations with Polynomials? (+FREE Worksheet!)"?

No one replied yet.

Leave a Reply