Exploring Adding and Subtracting Rational Expressions

This video tutorial covers the multiplication of polynomials, focusing on binomials and trinomials. It introduces the FOIL method as a systematic approach to distribute terms and combine like terms. The tutorial includes several examples, ranging from basic to advanced, demonstrating the application of the FOIL method. Additionally, it explores multiplying binomials with trinomials and provides a geometric application to find the area of a shaded region using polynomial multiplication.

What is the first step in the FOIL method?

• Add the coefficients

• Distribute the outer term

• Combine like terms

• Multiply the inner terms

In the expression (x + 2)(x + 4), what is the result of the first distribution step?

• x^2 + 6x

• x^2 + 4x

• x^2 + 2x

• 2x + 4

What is the result of combining like terms in the expression x^2 + 4x + 2x + 8?

• x^2 + 6x + 8

• x^2 + 4x + 8

• x^2 + 2x + 8

• x^2 + 8x + 8

What is the result of (4x - 7)(x + 3) after combining like terms?

• 4x^2 + 5x - 21

• 4x^2 - 5x - 21

• 4x^2 + 7x - 21

• 4x^2 - 7x - 21

What is the result of squaring the binomial (x + 4)?

• x^2 + 4x + 16

• x^2 + 8x + 16

• x^2 + 4x + 8

• x^2 + 8x + 8

What is the first step when multiplying a binomial with a trinomial?

• Add the coefficients

• Combine like terms

• Multiply the inner terms

• Distribute the outer term

In the expression (x + 4)(x^2 + 3x - 6), what is the result of the first distribution step?

• x^3 + 3x^2 - 6x

• x^3 + 4x^2 - 6x

• x^3 + 3x^2 + 4x

• x^3 + 4x^2 + 3x

What is the result of combining like terms in the expression x^3 + 3x^2 + 4x^2 - 6x + 12x - 24?

• x^3 + 7x^2 + 6x - 24

• x^3 + 7x^2 - 6x - 24

• x^3 + 3x^2 + 6x - 24

• x^3 + 7x^2 + 6x + 24

What is the first step in finding the area of the shaded region in the geometric application?

• Subtract the area of the inside region

• Distribute the outer term

• Combine like terms

• Multiply the inner terms

In the geometric application, what is the result of distributing 9x to 2x and 7?

• 18x^2 + 63x

• 18x^2 + 7x

• 9x^2 + 63x

• 9x^2 + 7x