How to Multiply and Divide Expressions

Be efficient with your coefficients.

Difficulty:

Moderately Easy

Instructions

Things You'll Need

• Calculators
• Desk Lamps
• Desks

Polynomial Expressions

1. Multiply the first term of the first polynomial by the first term of the second polynomial. The product is the first term of your answer.

2. Multiply the first term of the first polynomial by the second term of the second polynomial. The product is the second term of your answer.

3. Multiply the first term of the first polynomial by the third, fourth and so on terms of the second polynomial until all terms of the second polynomial have been multiplied.

4. Repeat the previous three steps for the remaining terms of the first polynomial.

5. Simplify your answer by combining like terms.

Single-Term Expressions

1. Multiply two like terms by multiplying the coefficients together to get a new coefficient, and then add the exponents together to get a new exponent.

2. Divide two like terms by dividing the coefficient of the dividend by the coefficient of the divisor to get a new coefficient. Subtract the exponent of the variable in the divisor from the exponent of the variable in the dividend to get a new exponent.

3. Multiply two unlike terms by multiplying the coefficients together to get a new coefficient and writing the variables next to each other.

4. Divide two unlike terms by dividing the coefficient of the dividend by the coefficient of the divisor to get a new coefficient. The new variable will be a fraction in which the numerator is the variable of the dividend and the denominator is the variable of the divisor.

Tips & Warnings

• Example: (2x + 3)(y - 6) = 2xy - 12x + 3y - 18

• Example 1: (2x)(3x) = 6x^2

• Example 2: (4x^3)/(2x^2) = 2x

• Example 3: (4x)(8y) = 32xy

• Example 4: (10x)/(2y) = 5(x/y)