Multiply a Monomial and 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

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2. Multiply​

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3. Simplify​

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Multiply a Polynomial by a Monomial

Vertical Method:​ -3x²(7x²-x+4)

​1. Stack

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2. Multiply with Distributive Property

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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!​

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Add the polynomials​

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Fill in the Blanks

Challenge: Solve for a

$2a\left(5a-2\right)+3a\left(2a+6\right)+8=a\left(4a+1\right)+2a\left(6a-4\right)+50$  

Correct answers get a piece of candy!

Multiply Binomials: FOIL

Multiply Binomials: FOIL

​​(2y-7)(3y+5)

F irst

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O utside

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I nside

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L ast​

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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