Exploring Adding and Subtracting Rational Expressions

This video tutorial covers the basics of monomials and polynomials, including their definitions and classifications. It explains various exponent rules such as the product, power, quotient, negative exponent, and zero exponent rules, with examples. The tutorial also demonstrates how to simplify monomials and perform operations like adding, subtracting, and multiplying polynomials. Finally, it includes a word problem to apply these concepts in a practical scenario.

Which of the following is an example of a monomial?

• x^2 + y^2

• 5x^2 - 3x + 1

• 3x + 2

• 7x

According to the product rule, what is x^3 * x^7?

• x^4

• x^21

• x^10

• x^14

What does x^0 equal?

• 1

• 0

• x

• Undefined

Simplify: 5^0 / 3^-1 all raised to the power of -2.

• 1/9

• 9

• 1/81

• 81

What is the result of 57x^4y^-2 / 3xy^-3?

• 19x^3y

• 19x^3y^-1

• 19x^3y^5

• 19x^3y^2

What is a polynomial with a degree of 2 called?

• Cubic

• Linear

• Quadratic

• Quartic

How many terms does a trinomial have?

• 4

• 3

• 2

• 1

Simplify: (3w^2 - 5w + 9) - (9 + 3w^2 + 7w).

• -12w + 18

• -12w - 15

• -5w - 15

• -5w + 18

What is the result of multiplying (2b - 3) and (2b + 3)?

• 4b^2 + 6b

• 4b^2 - 9

• 4b^2 + 9

• 4b^2 - 6b

Find the difference between the area of the original triangle and the new triangle if the base is tripled and the height is doubled.

• 37.5x^2 + 80x - 17

• 45x^2 + 96x - 21

• 37.5x^2 + 80x - 17.5

• 7.5x^2 + 16x - 3.5