A.2 Multiplying Polynomials

Multiplying Polynomials & Special Products

Multiple Choice

According to exponent rules, when we raise a power to another power we _______ the exponents.

• add

• subtract

• multiply

• divide

Multiple Choice

According to exponent rules, when we divide the expressions we _______ the exponents.

• add

• subtract

• multiply

• divide

Multiple Choice

According to exponent rules, when we multiply terms with the same base we _______ the exponents.

• Multiply

• Add

• Divide

• Subtract

Multiple Choice

Simplify:

$$5\left(3x+2\right)$$  

• $$3x+10$$

• $$15x+10$$  

• $$15x-10$$  

• $$3x-10$$  

Multiplying Polynomials

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.

Watch the video and show your work on a piece of paper for EVERY questions in the Quizizz. You must turn your work in as a part of your grade.

Get a piece of paper and pencil ready!

Here is another way to multiply polunomials

You can pick whichever method you think works best for you, but... box method will set you up for success later! ^_^

​Box Method

Multiple Select

$$\left(x\ +\ 4\right)\left(x\ +\ 8\right)$$  Multiply:

• $$x^2\ +\ 12x\ +\ 32$$  

• $$32x^2$$  

• $$x^2\ +\ 32$$  

Multiple Select

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

• $$6x^2\ +\ 13x\ +\ 6$$  

• $$6x^2\ +\ 6$$  

• $$5x^2\ +10x\ +5$$  

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

Multiply.
(x + 2)(x + 3)

• x² + 5x + 6

• x² + x + 6

• x² + 5x + 5

• x² + 6x + 6

Multiple Choice

Simplify:
2x (-2x - 3)

• -4x - 3

• x² - 3

• -4x² - 6x

• -4x - 6

Perfect Squares:

Multiple Choice

Multiply:

$$\left(x+3\right)^2$$  

**Start by rewriting as (x+3)(x+3)**

• $$x^2+6x+9$$  

• $$x^2+9$$  

• $$x^2+3x+9$$  

• $$x^2+6x+6$$  

Multiple Choice

(x + 5)² 

Hint: try (x + 5)(x + 5)

• x² + 25

• x² + 10x + 25

• x² + 10 x + 10

• x² + 10

Multiple Choice

Simplify:

(x-7)²

• x²-49

• x²+49

• x²-14x+49

• x²-14x-49

Multiple Choice

Find the product.

(x - 2)²

• x² + 2x + 2x + 4

• x² + 2x + 2

• 7x² + x + 7

• x² - 4x + 4

Multiple Choice

Find the area of a rectangle with length (x - 5) and width (3x + 1).

• 3x²+16x-5

• 3x²-14x+5

• 3x²-14x-5

Box method example

The box method works with different combinations of polynomials.

(image: 4 term polynomial multiplying a Trinomial!)

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

(5x-1)(x+1)

• 5x² + 4x - 1

• 5x²+6x - 1

• 5x² - 4x -1

• 5x² + 4x + 1

Multiple Choice

(3x − 6)(7x + 7)

• 21x² − 63x + 42

• 21x² − 21x − 42

• 21x² − 42

• 21x² + 63x + 42

Multiple Choice

4a(5a² - a + 4)

• 20a³ - 4a² + 16a

• 20a² - 5a + 8a

• 20a² + 4a² + 16a

• 20a³ +3a² + 16a

Multiple Choice

(x+7)(3x+2)

• 3x² + 10x + 14

• 3x² + 14

• 4x + 9

• 3x² + 23x +14

Multiple Choice

(a+b)(a+b)

• a² - b²

• a² + b²

• a² + ab + b²

• a² + 2ab + b²

Multiple Choice

(5x-1)(x+1)

• 5x² + 4x - 1

• 5x² + 6x - 1

• 5x² - 4x - 1

• 5x² + 4x + 1

Multiple Choice

(5x-1)(x+1)

• 5x² + 4x - 1

• 5x²+6x - 1

• 5x² - 4x -1

• 5x² + 4x + 1

Multiple Choice

(x - 6)(2x + 3)

• 2x² - 9x - 18

• 2x² + 15x - 18

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

(x+10)(x-10)

• x²  - 100

• x² + 100

• x² + 20x - 100

• x² -20x + 100

Multiple Choice

(3x - 5)(x² - 5x +6)

• 3x³ - 20x² + 43x - 30

• 3x^{2 -} - 43x

• 3x³ -25x -30

• 3x³ +25x

Multiple Choice

Find the product.

(x - 2)²

• x² + 2x + 2x + 4

• x² + 2x + 2

• 7x² + x + 7

• x² - 4x + 4

Multiple Choice

(x + 7)(x + 9)

• x² + 63x + 16

• x² + 16x + 63

• x² + 79

• x² + 16x + 2

Multiple Choice

Find the product: (y - 3)(y + 7)

• y² - 21

• y² + 10x - 21

• y² + 4y - 21

• 2y - 10

• 2y + 4

Multiple Choice

Now give this one a try:

Multiply (5x-3)(5x+3)

• 25x²-15x-9

• 25x²+15x-9

• 25x²-9

• 25x²+9