Polynomial Multiplication

Multiplying Polynomial Expressions

by Sahel Otoom

Multiple Choice

Warm Up

 A rectangular picture frame has the dimensions shown inthe figure. Write a polynomial that represents the perimeter

of the frame.

• 16x-2

• 8x-2

• 7x+3

• 16x+2

​Objectives

​ Multiply polynomials.

Use binomial expansion to expand binomial expressions that are raised to positive integer powers.​

​To multiply a polynomial by a monomial, use the Distributive Property and the Properties of Exponents.

​EQ: How do you work with polynomials to rewrite expressions and solve problems?

​Area Method

​https://youtu.be/oOTFGdjhqqM

Multiple Choice

Write the area of rectangle as a product of two binomials.

• A=(−10x)(12x)

• A=(3x+4)(2x−5)

• A=6x+20

• A=6x−20

Multiple Choice

Write the area of the rectangle in expanded form.

• A=6x−60

• A=7x+7

• A= 6 $$x^2$$  − 18x −60

• None

Multiple Choice

• Step 1, Should add like terms to get the inside values.

• Step 1, combining 2x and 3x should equal 5x.

• Step 3, Combined like terms incorrectly.

• No errors were made.

​Distribution Method

​https://youtu.be/Xy8NKUoyy98

Multiple Choice

• Step 1, cannot distribute an expression with more than one term.

• Step 2, cannot use commutative property with multiplication.

• Step 3, distributed incorrectly.

• Step 4, did not combine like terms correctly.

• Ana got the correct answer.

Multiple Choice

Expand the expression:

(2n+1)(n−7)  

• 3n−6  

• 3n+6  

• $$2n^2-13n-7$$  

• $$2n^2+13n-7$$

Multiple Choice

Expand the expression: 

(7v−2)(6v+5)  

• $$42v^2+23v-10$$  

• $$42v^2+23v+10$$

• $$4v^2+23v-10$$

• $$v^2+23v+2$$

​FOIL Method

​https://youtu.be/Axv7cqezipY

Multiple Choice

What does FOIL stand for?

• Failing Only in Latin
• Farming Only in Lakewood
• First Outside Inside Last
• Fresh Only in Lakes

Multiple Choice

(2x - 1)(x + 2)

• 2x² + 3x - 2

• 2x² - 5x - 2

• 2x² + 3x + 2

• 2x² - 5x + 2

Multiple Choice

Mult (2x + 3)(3x + 4)

• 6x² + 17x + 7

• 6x² + 17x + 12

• 6x² + 8x + 12

• 6x² + 9x + 12

Multiple Choice

(x + 12)(x - 12)

• x^2 - 144
• x^2 + 144
• x^2 + 12x - 144
• x^2 - 12x + 144

Multiple Choice

(x - 6)^2

• x^2 - 12x + 36
• x^2 + 36
• x^2 - 36
• x^2 - 6x + 36

Multiple Choice

(x - 7)(x + 7)

• x^2 + 7x - 49
• x^2 - 7x + 49
• x^2 - 49
• x^2 + 49

Multiple Choice

If each side of a square is (x - 3), find the area of the square.

• 2x - 6

• 4(x - 3)

• x² - 6x + 9

• x² - 9