Multiply a Monomial by a Polynomial

8.2/8.3 Multiplying Polynomials

Multiply a Polynomial by a Monomial

Horizontal Method:​ -3x²(7x²-x+4)

​1. Rewrite with Distributive Property

​

2. Multiply​

​

3. Simplify​

​

Multiply a Polynomial by a Monomial

Vertical Method:​ -3x²(7x²-x+4)

​1. Stack

​

​

​

2. Multiply with Distributive Property

​

​

Multiple Choice

Simplify the expression.
-3x²( 7x² - x + 4)

• -21x⁴ + 3x³ -12x²
• 7x² - x + 4 (-3x²)
• 21x⁴ + 3x³ + 12x²
• -12x² + 3x³ -21x⁴

2p(-4p²+5p) - 5(2p²+20)

Simplify

Two steps:

Distribute First!​

​

​

​

Add the polynomials​

​

​

​

Multiply Binomials: FOIL

Multiply Binomials: FOIL

​​(2y-7)(3y+5)

F irst

​

O utside

​

I nside

​

L ast​

​

Multiply Binomials: Distribute

​​(2x+3)(x+5)

Multiple Choice

Find the product:

(x+5)(x+2)

• $$x^2+7x+10$$  

• $$x^2+10$$  

• $$2x+7$$  

• $$x^2+5x+2$$  

Multiply Polynomials: Distribute

​​(6x+5)(2x²-3x-5)

Multiple Choice

Find the product:

$$\left(2a-9\right)\left(3a^2+4a-4\right)$$  

• $$6a^2-63a+36$$  

• $$6a^3-10a^2-40a+32$$  

• $$6a^3-19a^2-44a+36$$  

• No solution