Multiplying a Multiplying a polynomialpolynomial

by a monomial.by a monomial.By: India ShepardBy: India Shepard

And Ryan PetersonAnd Ryan Peterson

What is this about??What is this about??

This topic is about using the This topic is about using the distributive property to find a solution.distributive property to find a solution.

Sometimes there is more than one Sometimes there is more than one number or variable being distributed number or variable being distributed into the “( )”.into the “( )”.

You must simplify until no more You must simplify until no more exponets can be added and all like exponets can be added and all like terms are combined.terms are combined.

Method 1.Method 1.

-2x-2x22(3x(3x22-7x+10) Tips: multiply -7x+10) Tips: multiply numbersnumbers

Distributing! Distributing! NotNot exponents! exponents!

-2x²(3x²)= -6x4 and don’t leave out-2x²(3x²)= -6x4 and don’t leave out

-2x²(-7x)= 14x³ negatives.-2x²(-7x)= 14x³ negatives.

-2x²(10)= -20x²-2x²(10)= -20x²

Combine!Combine!

-6x4+14x³-20x²-6x4+14x³-20x²

Method 2.Method 2.

(Vertical method) you take -2x² (Vertical method) you take -2x²

(vertically) and (vertically) and

multiply to multiply to each #. each #.

(3x²-7x+10)(3x²-7x+10) (x) -2x²(x) -2x² -6x²+14x³-20x²-6x²+14x³-20x²

Practice ProblemsPractice Problems

1.1. w(2w³-9w²) 8.-3y(5y+2) w(2w³-9w²) 8.-3y(5y+2)

2.2. 5y(-2y²-7y) 9. t(5t-9)-2t5y(-2y²-7y) 9. t(5t-9)-2t

3. -3np(n²-2p) 10. 3. -3np(n²-2p) 10. x(3x+4)+2(7x-3 x(3x+4)+2(7x-3

4.4. 6x³(5+3x-11x²)6x³(5+3x-11x²)

5.5. Cd²(3d+2c²d-4c)Cd²(3d+2c²d-4c)

6.6. -x(4x²-2x)-5x³-x(4x²-2x)-5x³

7.7. 5n(2n³+n²+8) +n(4-n)5n(2n³+n²+8) +n(4-n)

Answers:Answers:

1.2w1.2w³ -9w³ 10.3x² + 18x - 6 ³ -9w³ 10.3x² + 18x - 6 2. -10y³-35y²2. -10y³-35y²3. -3n³p + 6np3. -3n³p + 6np4.30x³ + 18x4.30x³ + 18x4 4 – 66x– 66x55

5.3cd³ + 2c³d³ - 4c²d²5.3cd³ + 2c³d³ - 4c²d²6.-4x³+ 2x² - 5x6.-4x³+ 2x² - 5x7. 10n7. 10n4 4 ++ 5n³ + 44n5n³ + 44n8. 15y² - 6y8. 15y² - 6y9.5t² - 11t² 9.5t² - 11t²

ResourcesResources

www.algebra1.comwww.algebra1.com

http://nlvm.usu.edu/en/nav/vlibrary.htmlhttp://nlvm.usu.edu/en/nav/vlibrary.html

http://www.glencoe.com/sec/math/prealg/http://www.glencoe.com/sec/math/prealg/prealg05/study_guide/pdfs/prealg_pssg_G111.pdf prealg05/study_guide/pdfs/prealg_pssg_G111.pdf

http://www.tutornext.com/multiplication-division-http://www.tutornext.com/multiplication-division-polynomials/880 polynomials/880

http://faculty.stcc.edu/zee/newpage121.htmhttp://faculty.stcc.edu/zee/newpage121.htm

Summary tools!Summary tools!

When you are solving this type problem you can When you are solving this type problem you can use the use the distributive propertydistributive property to solve. to solve.

When solving these problems it is important to When solving these problems it is important to watch your watch your symbols symbols and watch your and watch your negatives negatives and and positives.positives.

When doing the problems using calculator will help When doing the problems using calculator will help you so you don’t make a mistake with mixing up you so you don’t make a mistake with mixing up what’s suppose to be positive and negative.what’s suppose to be positive and negative.

When distributing remember make your variables When distributing remember make your variables exponents if there are two or more being exponents if there are two or more being multiplied. multiplied.