Multiplying Polynomials Box Method

Multiplying Polynomials

Today we are going to learn how to multiply two polynomials.

But first...

Open Ended

Simplify.

$$2\left(x+4\right)$$  

Open Ended

Simplify.

$$-3\left(2-5x\right)$$  

Open Ended

Simplify.

$$\left(3x\right)\left(-4x\right)$$  

Box Method

This is a very useful method and learning to use the box method to multiply will be very helpful in our next unit which is factoring polynomials.

Multiplying by a monomial.

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Multiplying by a monomial.

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Open Ended

Simplify.
$$\left(3x\right)\left(2x^2-4x+3\right)$$  

Open Ended

Simplify.
$$-2x^2\left(6-2x+4x^2\right)$$  

​Multiply (x+4)(x+8)

​Multiply (3x+4)(2x+5)

Multiple Select

$$\left(2x\ +\ 3\right)\left(3x\ +\ 2\right)$$  

• $$6x^2\ +\ 13x\ +\ 6$$  

• $$6x^2\ +\ 6$$  

• $$5x^2\ +10x\ +5$$  

​Multiply (3x-4)(2x²+5)

Multiple Select

$$\left(2x^{ }\ -\ 5\right)\left(x\ +\ 4\right)$$  

• $$2x^2\ +3x\ -20$$  

• $$2x^2\ -\ x\ -20$$  

• $$x^2\ -\ 20$$  

• $$x^2\ +\ 13x\ -20$$  

Multiple Choice

$$\left(2x+1\right)\cdot\left(4x-1\right)$$  

Multiply the binomials using the BOX method.

Choose the correct "box".

Multiple Choice

(3x − 6)(7x + 7)

• 21x² − 63x + 42

• 21x² − 21x − 42

• 21x² − 42

• 21x² + 63x + 42

​Multiply (3x+3)(x²-2x+6)

Multiple Choice

(5x+2)(x²-3x+6)

• 5x³ - 17x² +24x +12

• 5x³ + 17x² - 24x +12

• 5x³ - 13x² + 24x +12

• 5x³ +13x² - 24x - 12

Multiple Choice

(2m-5)²

• 4m^2 - 20m + 25

• 4m^2-20m+25

Multiple Choice

Multiply:
(5x+2)(x²-3x+6)

• 5x³ - 17x² +24x +12
• 5x³ + 17x² - 24x +12
• 5x³ - 13x² + 24x +12
• 5x³ +13x² - 24x - 12

Multiple Choice

Multiply:
(5c-2)(3c²-5c+4)

• 15c³-31c⁴+30c²-8
• 15c³-19c²+10c-8
• 15c³-31c²+30c-8
• 15c³-31c²+30c+8

Multiple Choice

Multiply:
(2x−9)(2x+9)

• 2x²+81
• 2x²−81
• 4x²+81
• 4x²−81

Multiple Choice

Find the product:
(x+7)(x−7)

• x²−14x−49
• x²−49
• x²+49
• x²+14x−49

Multiple Choice

(3x − 6)(7x + 7)

• 21x² − 63x + 42
• 21x² − 21x − 42
• 21x² − 42
• 21x² + 63x + 42

Multiple Choice

(5x+2)(x²-3x+6)

• 5x³ - 17x² +24x +12
• 5x³ + 17x² - 24x +12
• 5x³ - 13x² + 24x +12
• 5x³ +13x² - 24x - 12