Exploring Polynomial and Monomial Multiplication

This video tutorial covers the multiplication of polynomials, focusing on using the distributive property and product rule. It explains how to multiply monomials with binomials and trinomials, and how to simplify expressions by combining like terms. The tutorial also applies these skills to geometric problems, such as finding the area of triangles and trapezoids. Students are encouraged to practice these skills independently and check their understanding in class.

What is the product rule for multiplying exponents with the same base?

• Multiply the exponents

• Add the exponents

• Subtract the exponents

• Divide the exponents

When multiplying 3x^2y by 5x^3, what is the coefficient of the resulting term?

• 12

• 8

• 15

• 10

What is the result of multiplying 3x^2y by 2xy^2?

• 5x^2y^3

• 6x^2y^3

• 5x^3y^3

• 6x^3y^3

What is the simplified form of 3w * (-6w^2)?

• -18w^2

• 18w^3

• -18w^3

• 18w^2

What is the simplified form of 3w * 2w?

• 5w

• 6w

• 6w^2

• 5w^2

What is the formula for the area of a triangle?

• Base times height

• Base times height divided by 2

• Base plus height

• Base plus height divided by 2

If the base of a triangle is 4x^2 and the height is 5x - 2, what is the expression for the area before simplification?

• (4x^2 + 5x - 2) / 2

• (4x^2)(5x - 2) / 2

• (4x^2)(5x - 2)

• (4x^2 + 5x - 2)

What is the simplified form of the expression 20x^3 - 8x^2 divided by 2?

• 20x^3 - 8x^2

• 10x^3 - 8x^2

• 10x^3 - 4x^2

• 20x^3 - 4x^2

What is the result of distributing -3x^6 to 4x^2?

• 12x^6

• -12x^6

• 12x^8

• -12x^8

What is the simplified form of the expression 3x^3 + 4x^2 - 2x + 5 after distributing 3x^3?

• 9x^6 + 12x^5 - 6x^4 + 15x^3

• 9x^6 + 12x^5 - 6x^4 + 5

• 9x^6 + 12x^5 - 6x^4 + 15

• 9x^6 + 12x^5 - 6x^4