Multiplier Rule

Multiplying Polynomials

Rule # 1: Multiplying with exponents

Multiple Choice

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

• Multiply

• Add

• Divide

• Subtract

Rule #2: Raising a power to a power

Multiple Choice

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

• add

• subtract

• multiply

• divide

​Distributive Property: 
a(b + c) = ab + ac ​ or a(b - c) = ab - ac

​Example 1

​4(x + 8)
4(x) + 4(8)
4x+32

​

Example 2
3(3x - 7)
3(3x)-3(7)
9x-21

Multiple Choice

Simplify:

$$5\left(3x+2\right)$$  

• $$3x+10$$

• $$15x+10$$  

• $$15x-10$$  

• $$3x-10$$  

Fill in the Blanks

Simplify: -6(3x - 9)

​EXAMPLE

​6x²(3x - 4y)

6x²(3x)-6x²(4y) Multiply Both Terms by 6x²

6(3)(x²)(x¹) - (6)(4)(x²)(y) Multiply Coefficients

18(x²⁺¹) - 24x²y Add Exponents with same bases

18x³-24x²y

Math Response

Multiply: 6x³(x - 4)

Type answer here

Correct Answer: 6x^4-24x^3

Deg^°

Rad

Multiply Monomials

Multiple Select

Multiply: 3x(2x³)

• 6x⁴

• 5x³

• 5x⁴

• 6x³

Monomial times a polynomial

Multiple Choice

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

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

Multiplying Binomials

• Binomials have 2 terms:

  • Ex: (x + 4) or (5y + 2)

​

• Consists of a combo of

  • Distributive and

  • Combining Like Terms

Multiple Choice

Find the Product.

(3p - 3)(p - 1)

• 3p² + 6p + 3

• 3p² - 6p + 3

• 3p² - 6p - 3

• 3p² + 6p - 3

​Box Method

Multiple Choice

Find the product: (3x – 1)(x + 5) 

• 3x² + 4x + 5
• 3x² + 4x - 5
• 3x² + 14x + 5
• 3x² + 14x - 5

​Box Method (another example)

Multiple Select

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

• $$x^2\ +\ 12x\ +\ 32$$  

• $$32x^2$$  

• $$x^2\ +\ 32$$  

Multiple Select

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

• $$2x^2\ +3x\ -20$$  

• $$2x^2\ -\ x\ -20$$  

• $$x^2\ -\ 20$$  

• $$x^2\ +\ 13x\ -20$$  

Review Classifying Polynomials

• One term - Monomial:

  • x or -7x² or 5

• Two terms - Binomial

  • (x+5) or (3x² - 6)

• Three terms - Trinomial

  • (x² + 3x - 18) or (7x³ + 5x - 2)

• More than 3 terms - Polynomial

• Always write in standard form

  • Exponents decrease in order.

Multiple Choice

Which polynomial is written in standard form?

• -3x + 8x² + 9x³ - 11

• 9x³ + 8x² - 3x - 11

• 8x² + 9x³ -11 - 3x

• -11 - 3x + 8x² + 9x³

Multiple Choice

4x² + 8x - 7 has a degree of...

• Linear

• Constant

• Quadratic

• Cubic

Multiple Choice

Classify by number of terms:
3x³ – 6x

• Monomial
• Binomial
• Trinomial
• 4-Term Polynomial