Exploring Adding and Subtracting Rational Expressions

This video tutorial covers the multiplication of polynomials, focusing on multiplying monomials and polynomials. It begins with an introduction to the concept, followed by detailed examples that demonstrate the process of distributing terms and applying the product rule of exponents. The tutorial progresses to more complex examples, including combining like terms and solving for the area of a shaded region using polynomial multiplication. The video emphasizes the importance of taking a step-by-step approach to ensure accuracy.

What is the product rule of exponents when multiplying X^a and X^b?

• a - b

• a / b

• a * b

• a + b

What is the result of distributing x over (x + 4)?

• x^2 + 4x

• x^2 + 4

• x^2 + 4x^2

• x + 4x

When distributing -3n over (1 + 2n - 8), what is the coefficient of the n^2 term?

• -6

• 3

• 6

• -3

In the expression 5n^3(3n^2 - n - 7), what is the coefficient of the n^5 term?

• 3

• 35

• 5

• 15

When distributing 5 over (3r^2s + r^2s^2 - 4s), what is the coefficient of the r^2s^2 term?

• 5

• 15

• 20

• 10

What is the result of distributing y over (y + 4) and then distributing -y over (y - 3)?

• y^2 + 4y - y^2 - 3y

• y^2 + 4 - y^2 + 3y

• y^2 + 4y - y^2 + 3y

• y^2 + 4y - y^2 + 3

In the expression -2x(5x + 3), what is the coefficient of the x term?

• -6

• -3

• -10

• -2

What is the simplified form of 4x^2 + 4x - 20x^2 - x^3 + 3x?

• -x^3 - 16x^2 + 7x

• -x^3 - 16x^2 + 3x

• -x^3 - 16x^2 + 4x

• -x^3 - 16x^2 + 6x

How do you find the area of the shaded region if the total area is 6x(8x - 1) and the inner box is 2x(5x + 3)?

• Divide the total area by the area of the inner box

• Subtract the area of the inner box from the total area

• Add the area of the inner box to the total area

• Multiply the area of the inner box by the total area

What is the simplified form of 48x^2 - 6x - 10x^2 - 6x?

• 38x^2 - 1x

• 38x^2 - 2x

• 38x^2 - 6x

• 38x^2 - 12x