When we multiply two or more polynomials together, we use our associative, commutative, and distributive properties. Basically, the simplest operation occurs when we multiply a monomial by another monomial. To perform this operation, we multiply the number parts together and the variable parts together. As we move into more difficult problems, such as a binomial times another binomial, we need to use our distributive property to ensure each term of the first polynomial (leftmost) is multiplied by each term of the second polynomial (rightmost). When we have something such as the product of two binomials, we can use a common shortcut known as FOIL (first terms, outer terms, inside terms, and last terms).

Test Objectives
• Demonstrate an understanding of the rules of exponents
• Demonstrate the ability to multiply a monomial by a polynomial
• Demonstrate the ability to use FOIL to multiply two binomials
• Demonstrate the ability to multiply more than two polynomials
Multiplying Polynomials Practice Test:

#1:

Instructions: Find each product.

$$a)\hspace{.2em}2(4x + 2)$$

$$b)\hspace{.2em}5x^3(3x + 2)$$

#2:

Instructions: Find each product.

$$a)\hspace{.2em}(3x - 2)(3x - 2)$$

$$b)\hspace{.2em}(x + 5)(4x - 1)$$

#3:

Instructions: Find each product.

$$a)\hspace{.2em}(4x + 4)(5x + 3)$$

$$b)\hspace{.2em}(5x + 2)(2x + 3)$$

#4:

Instructions: Find each product.

$$a)\hspace{.2em}(2x^2 - 3x - 4)(5x - 1)$$

$$b)\hspace{.2em}(5x^2 - 3x - 1)(4x - 1)$$

#5:

Instructions: Find each product.

$$a)\hspace{.2em}(6x^2 + 6xy - 8y^2)(7x + y)$$

$$b)\hspace{.2em}(x^2 - xy - 5y^2)(2x^2 - 5xy + 2y^2)$$

Written Solutions:

#1:

Solutions:

$$a)\hspace{.2em}8x + 4$$

$$b)\hspace{.2em}15x^4 + 10x^3$$

#2:

Solutions:

$$a)\hspace{.2em}9x^2 - 12x + 4$$

$$b)\hspace{.2em}4x^2 + 19x - 5$$

#3:

Solutions:

$$a)\hspace{.2em}20x^2 + 32x + 12$$

$$b)\hspace{.2em}10x^2 + 19x + 6$$

#4:

Solutions:

$$a)\hspace{.2em}10x^3 - 17x^2 - 17x + 4$$

$$b)\hspace{.2em}20x^3 - 17x^2 - x + 1$$

#5:

Solutions:

$$a)\hspace{.2em}42x^3 + 48x^2y - 50xy^2 - 8y^3$$

$$b)\hspace{.2em}2x^4 - 7x^3y - 3x^2y^2 + 23xy^3 - 10y^4$$