Multiplying Polynomials Using an Area Model

This video tutorial teaches how to multiply polynomials using an area model. It begins with a review of multiplying monomials, emphasizing the importance of multiplying coefficients, keeping the base, and adding exponents. The tutorial then addresses common misunderstandings in polynomial multiplication, such as incorrectly multiplying only like terms. Through examples, it demonstrates the use of an area model to multiply binomials and larger polynomials, highlighting the process of combining like terms to simplify the result. The lesson concludes with a comprehensive example, reinforcing the method's applicability to polynomials of any size.

What is the first step in multiplying monomials?

• Add the exponents

• Multiply the coefficients

• Subtract the exponents

• Divide the coefficients

Why can't you simply multiply like terms when multiplying polynomials?

• Because it only works for monomials

• Because it ignores the distributive property

• Because it results in negative exponents

• Because it only applies to addition

In the area model, what is the result of multiplying 4x by 5x?

• 20x squared

• 9x squared

• 20x

• 9x

What is the final result of multiplying 5x + 2 by 4x - 7 using the area model?

• 20x squared + 27x + 14

• 20x squared - 27x - 14

• 20x squared - 14

• 20x squared - 27x + 14

What is the final simplified result of multiplying 3x cubed + 12x squared - 8x + 2 by 4x - 1?

• 12x to the fourth + 45x cubed - 44x squared + 16x + 2

• 12x to the fourth + 45x cubed + 44x squared + 16x - 2

• 12x to the fourth + 45x cubed - 44x squared - 16x - 2

• 12x to the fourth + 45x cubed - 44x squared + 16x - 2