Multiplying Monomials and Polynomials

Multiplying Monomials and Polynomials

Read each question carefully and show all your work. Simplify your answers as much as possible.

1. Simplify the following expressions:

a) (3x^2)(5x^3)

b) (-7y^4z)(-2yz^3)

c) (4ab^2c^3)(6a^2bc)

2. Fill in the blanks to complete the multiplication:

a) 2x(3x + 5) =   +  

b) -4y(y^2 - 2y + 7) =   +   +  

c) 5a^2(a^3 - 4a + 2) =   -   +  

3. Expand and simplify the following binomial products:

a) (x + 3)(x + 5)

b) (2y - 1)(y + 4)

c) (3a - 2)(3a + 2)

4. What is the expanded form of (x - 2)(x^2 + 3x - 1)?

5. A rectangular garden has a length of (2x + 3) meters and a width of (x - 1) meters. Write an expression for the area of the garden in terms of x. Simplify your answer.

6. State whether each statement is True or False:

a) The product of a monomial and a binomial is always a binomial.

b) (x + y)^2 = x^2 + y^2