Simplifying Polynomials and Combining Like Terms

In this Math Antics video, Rob introduces the concept of simplifying polynomials by combining like terms. He begins with a recap of polynomials and explains that simplifying involves identifying terms with the same variable part. Using a fruit analogy, Rob illustrates why only like terms can be combined. The video includes a game to practice identifying like terms and provides examples of simplifying complex polynomials. Rob concludes by encouraging viewers to practice simplifying polynomials on their own.

What are polynomials composed of?

• Variables only

• Chains of terms added or subtracted together

• Single terms multiplied together

• Numbers only

What is the process of combining terms with the same variable part called?

• Multiplying Terms

• Combining Like Terms

• Subtracting Terms

• Adding Terms

Why can we combine terms with the same variable part?

• Because they represent the same quantity

• Because they have different exponents

• Because they are constants

• Because they are in different orders

Are 2x and 3x like terms?

• No, because they are different variables

• Yes, because they have the same variable part

• No, because they have different coefficients

• Yes, because they are both first degree terms

Are 4x and 5y like terms?

• No, because they have different variable parts

• Yes, because they are both variables

• No, because they have different coefficients

• Yes, because they are both first degree terms

What is the result of combining 2x^2 and -7x^2?

• -9x^2

• -5x^2

• 5x^2

• 9x^2

Are 5xy and 8yx like terms?

• No, because they are in different orders

• Yes, because they are both variables

• No, because they have different coefficients

• Yes, because xy is the same as yx

Simplify the polynomial: x^2 + 6x - x + 10

• x^2 + 5x + 10

• x^2 + 5x + 9

• x^2 + 7x + 10

• x^2 + 6x + 10

Simplify the polynomial: 16 - 2x^3 + 4x - 10

• 16 - 2x^3 + 4x - 10

• 6 - 2x^3 + 4x

• 6 - 2x^3 - 4x

• 16 - 2x^3 - 4x - 10

What should you do first when simplifying a long polynomial?

• Combine all terms with the same degree

• Cross off terms that can't be combined

• Rearrange the terms in order of degree

• Look for like terms to combine