Apply multiplication and division rules

Learning Objectives Apply the product and quotient rules of exponents to simplify expressions with variables. Multiply polynomials, including binomials and trinomials, using the distributive property. Divide a polynomial by a monomial and a binomial. Simplify products and quotients of radical expressions. Multiply and divide rational expressions by factoring and canceling common factors. Identify non-permissible values when dividing rational expressions. Ever wonder how video game physics engines make characters jump and move realistically? 🎮 It all comes down to manipulating complex polynomial and rational functions! This tutorial focuses on the fundamental rules for multiplying and dividing the algebraic expressions you'll encounter in Grade 9, including polynomials...

TermDefinitionExample PolynomialAn expression consisting of variables and coefficients, involving only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.3x^2 - 7x + 2 is a trinomial (a type of polynomial). Radical ExpressionAn expression that contains a root (square root, cube root, etc.). The value inside the radical symbol is called the radicand.\sqrt{18x^3}, where 18x^3 is the radicand. Rational ExpressionA fraction in which the numerator and/or the denominator are polynomials. It is essentially a ratio of two polynomials.\frac{x^2 - 4}{x + 2} Exponent RulesA set of rules that govern how to perform operations on expressions with exponents. The Product Rule and Quotient Rule are key for multiplication and division.Product Rule: x^m...

Product Rule for Exponents x^a \cdot x^b = x^{a+b} When multiplying two powers with the same base, keep the base and add the exponents. Remember to multiply the coefficients separately. Quotient Rule for Exponents \frac{x^a}{x^b} = x^{a-b} \quad (for \ x \neq 0) When dividing two powers with the same base, keep the base and subtract the exponent of the denominator from the exponent of the numerator. Product Rule for Radicals \sqrt[n]{a} \cdot \sqrt[n]{b} = \sqrt[n]{ab} \quad (for \ a, b \ge 0) The product of two radicals with the same index (the small number indicating the root type) is equal to the radical of the product of their radicands. Division Rule for Rational Expressions \frac{A}{B} \div \frac{C}{D} = \frac{A}{B} \cdot \frac{D}{C} = \frac{AD}{BC} \quad...