Multiplying Monomials by a Polynomial

Multiplying Polynomials

Monomial x Polynomial

Monomial x Polynomial

This is basically just distribution!

Example: 5x(7x² - x + 3)
Recall the
product rule:
x^m∙xⁿ = x^m+n
35x¹⁺² - 5x¹⁺¹ + 15x¹

35x³ - 5x² + 15x

Example: x²(2x³ - x² + 7)

2x²⁺³ - x²⁺² + 7x²= 2x⁵ - x⁴ + 7x²

Example: 2xy(8x² + 4y² + 3xy)

16x¹⁺²y¹ + 8x¹y¹⁺² + 6x¹⁺¹y¹⁺¹

16x³y + 8xy³ + 6x²y²

Grab paper and pencil and write down work evidence, you will need to upload to Canvas after you finish.


NO WORK EVIDENCE = NO CREDIT!

Multiple Choice

4m(3m⁷ + 2m⁵)

• 7m⁷ + 6m⁶
• 12m⁸ + 8m⁶

Multiple Choice

Simplify:
3a(5a² + 8a + 2)

• 15a³ + 24a² + 6a
• 10a³ + 24a + 6
• 8a³ + 11a² + 6a
• 15a³ + 24a + 6

Multiple Choice

Multiply

Multiple Choice

5x(4x³ + 8)

• 9x⁴ + 40x

• 20x⁴ + 40x

• 20x³ + 40x

• 9x⁴ + 13x

Multiple Choice

Multiply

Multiple Choice

Simplify:
x²(2x+3)

• x²+2x+3
• 2x+3
• 2x²+3x
• 2x³+3x²

Multiple Choice

Multiply

Multiple Choice

3a(5a² + 8a + 2)

• 15a³ + 24a² + 6a
• 10a³ + 24a + 6

Multiple Choice

Multiply

Multiple Choice

Multiply

Multiple Choice

3x(2x² + 9x + 6)

• 6x³ + 27x² + 18x
• 6x³ + 18x² + 9

Multiple Choice

7y(5y² + 2y + 3)

• 35y³ + 14y² + 21y

• 12y³ + 14y² + 21y

• 35y³ + 14y² + 21

• 12y³ + 14y² + 10y

Multiple Choice

Multiply, then combine like terms:
$$2\left(x-1\right)-3x\left(4x-7\right)=$$  

• $$16x-2$$  

• $$12x^2-19x-2$$  

• $$12x^2-23x+2$$  

• $$-12x^2+23x-2$$  

Multiple Choice

Multiply, then combine like terms.
$$5a\left(4-6x\right)-3x\left(2+a\right)=$$  

• $$20a-33ax-6x$$  

• $$20a+23ax+6x$$  

• $$9a-14ax-x$$  

• $$9a+14ax+6x$$  

Multiple Choice

Multiply: 3m²n ( 4m² - 5n + 3 )

• 3m⁴n - 15m²n² + 9m²n

• 12m⁴n - 15m²n² + 9m²n

• 12m²n + 15m²n² - 9m²n

• 4m⁴n - 5m²n² + 3m²n

Multiple Choice

Multiply, then combine like terms:
$$2\left(x-3y+z\right)-3\left(-4x+2y+z\right)+4\left(-3x+y+2z\right)=$$  

• $$26x+16y+13z$$  

• $$2x^3-8y^3+7z^3$$  

• $$2x-8y+7z$$  

• $$26x^3+16y^3+13z^3$$  

Take a screenshot of score and upload to Canvas w/ Work Evidence