I am working on foiling section of my math the problem looks like (5x+2Y)(4X+Y) Book says answer is 20Xsquared+13xy+2y: I get all parts of the first and last terms in the answer statement but I have know idea how it foils out a 13xy term??

You have to multiply every term by BOTH of the other terms in the parentheses. 5x*4x(20x^2) + 5x*y(5xy)+4x*2y(8xy)+ y*2y(2y^2) =20x^2 + 13xy + 2y^2.

Is it okay if I use this method? : (9h+3)(-h-1) -h(9h+3)-1(9h+3) -9h^2-3h-9h-3 -9h^2-12h-3 This is what Sal showed in the multiplying binomials video.

Yes, you can double distribute with either the first or the second binomial, and you did it correctly. The answer will be the same if you did 9h(-h-1) + 3(-h-1), just that on your 3rd step, the -9h and -3h would be interchanged.

whats bigger than a quadratic equation?

Quadratic equations are equations with a variable to the second power. Cubic equations have something to the third, and quartic equations have a variable to the fourth. Quintic equations have a variable to the fifth, but they are unsolvable.

Use FOIL or extended distribution to complete the multiplication. You can find an explanation of FOIL in this video: https://www.khanacademy.org/math/algebra/introduction-to-polynomial-expressions/multiplying-binomials-2/v/multiplying-binomials Sal gave an example of extended distribution on the page above. See if you can follow the examples and work thru the problem. Comment back if you get stuck and tell me what you tried.

Is this method the same one as the foil one?

The method is same as foil but the better method is the method said by Sal

how is this going to help me count my money or get a job

That depends on what job you have - most majors in college require some math to graduate, so counting money as a burger flipper is easier than as an engineer because there is so much less to count. Even doctors and lawyers who have a lot of money to count must take math to get to where they are.

Main content

Algebra basics

Course: Algebra basics > Unit 7

Lesson 2: Multiplying binomials

Multiplying binomials review

Google Classroom

A binomial is a polynomial with two terms. For example, x, minus, 2 and x, minus, 6 are both binomials. In this article, we'll review how to multiply these binomials.

Example 1

Expand the expression.

left parenthesis, x, minus, 2, right parenthesis, left parenthesis, x, minus, 6, right parenthesis

Apply the distributive property.

\begin{aligned}&(\blueD{x-2})(x-6)\\ \\ =&\blueD{x}(x-6)\blueD{-2}(x-6)\\ \end{aligned}

Apply the distributive property again.

equals, start color #11accd, x, end color #11accd, left parenthesis, x, right parenthesis, plus, start color #11accd, x, end color #11accd, left parenthesis, minus, 6, right parenthesis, start color #11accd, minus, 2, end color #11accd, left parenthesis, x, right parenthesis, start color #11accd, minus, 2, end color #11accd, left parenthesis, minus, 6, right parenthesis

Notice the pattern. We multiplied each term in the first binomial by each term in the second binomial.

Simplify.

\begin{aligned} =&x^2-6x-2x+12\\\\ =&x^2-8x+12 \end{aligned}

Example 2

Expand the expression.

left parenthesis, minus, a, plus, 1, right parenthesis, left parenthesis, 5, a, plus, 6, right parenthesis

Apply the distributive property.

\begin{aligned} &(\purpleD{-a+1})(5a+6)\\\\ =&\purpleD{-a}(5a+6) +\purpleD{1}(5a+6) \end{aligned}

Apply the distributive property again.

equals, start color #7854ab, minus, a, end color #7854ab, left parenthesis, 5, a, right parenthesis, start color #7854ab, minus, a, end color #7854ab, left parenthesis, 6, right parenthesis, plus, start color #7854ab, 1, end color #7854ab, left parenthesis, 5, a, right parenthesis, plus, start color #7854ab, 1, end color #7854ab, left parenthesis, 6, right parenthesis

Notice the pattern. We multiplied each term in the first binomial by each term in the second binomial.

Simplify:

minus, 5, a, squared, minus, a, plus, 6

Want to learn more about multiplying binomials? Check out this video.

Practice

Problem 1

Current

Simplify.
Express your answer as a quadratic in standard form.

left parenthesis, x, plus, 1, right parenthesis, left parenthesis, x, minus, 6, right parenthesis

Want more practice? Check out this intro exercise and this slightly harder exercise.

Want to join the conversation?

Sort by:

Komal
Posted 6 years ago. Direct link to Komal's post “Is it okay if I use this ...”
Is it okay if I use this method? :
(9h+3)(-h-1)
-h(9h+3)-1(9h+3)
-9h^2-3h-9h-3
-9h^2-12h-3
This is what Sal showed in the multiplying binomials video.
Button navigates to signup pageButton navigates to signup page
(9 votes)
Answer
- David Severin
  Posted 6 years ago. Direct link to David Severin's post “Yes, you can double distr...”
  Yes, you can double distribute with either the first or the second binomial, and you did it correctly. The answer will be the same if you did 9h(-h-1) + 3(-h-1), just that on your 3rd step, the -9h and -3h would be interchanged.
  Button navigates to signup page
  (9 votes)
Jauneenm21
Posted 6 years ago. Direct link to Jauneenm21's post “I am working on foiling s...”
I am working on foiling section of my math the problem looks like (5x+2Y)(4X+Y) Book says answer is 20Xsquared+13xy+2y: I get all parts of the first and last terms in the answer statement but I have know idea how it foils out a 13xy term??
Button navigates to signup pageButton navigates to signup page
(10 votes)
Answer
- ∆, The #1 Ice-Cream Proponent
  Posted 6 years ago. Direct link to ∆, The #1 Ice-Cream Proponent's post “You have to multiply ever...”
  You have to multiply every term by BOTH of the other terms in the parentheses. 5x*4x(20x^2) + 5x*y(5xy)+4x*2y(8xy)+ y*2y(2y^2) =20x^2 + 13xy + 2y^2.
  Button navigates to signup page
  (6 votes)
charlybug2002
Posted 6 years ago. Direct link to charlybug2002's post “whats bigger than a quadr...”
whats bigger than a quadratic equation?
Button navigates to signup pageButton navigates to signup page
(3 votes)
Answer
- Hudson
  Posted 4 years ago. Direct link to Hudson's post “Quadratic equations are e...”
  Quadratic equations are equations with a variable to the second power.
  
  Cubic equations have something to the third, and quartic equations have a variable to the fourth. Quintic equations have a variable to the fifth, but they are unsolvable.
  Comment on Hudson's post “Quadratic equations are e...”
  (5 votes)
Nikolay
Posted 4 years ago. Direct link to Nikolay's post “For those interested, Q2 ...”
For those interested, Q2 can be simplified further (although the question doesn't want it).

(-6d+6)(2d-2)
= -6(d-1)x2(d-1)
= -12(d-1)(d-1)
= -12(d-1)^2
Button navigates to signup pageComment on Nikolay's post “For those interested, Q2 ...”
(4 votes)
Answer
ranoosh
Posted 6 years ago. Direct link to ranoosh's post “(4ab+2) (3ab-7)?”
(4ab+2) (3ab-7)?
Button navigates to signup pageButton navigates to signup page
(3 votes)
Answer
- Kim Seidel
  Posted 6 years ago. Direct link to Kim Seidel's post “Use FOIL or extended dist...”
  Use FOIL or extended distribution to complete the multiplication.
  You can find an explanation of FOIL in this video: https://www.khanacademy.org/math/algebra/introduction-to-polynomial-expressions/multiplying-binomials-2/v/multiplying-binomials
  
  Sal gave an example of extended distribution on the page above.
  
  See if you can follow the examples and work thru the problem. Comment back if you get stuck and tell me what you tried.
  Comment on Kim Seidel's post “Use FOIL or extended dist...”
  (2 votes)
LilPr33tz
Posted 6 years ago. Direct link to LilPr33tz's post “Does this mention trinomi...”
Does this mention trinomials
Button navigates to signup pageComment on LilPr33tz's post “Does this mention trinomi...”
(1 vote)
Answer
- Ampare
  Posted 6 years ago. Direct link to Ampare's post “It does not mention trino...”
  It does not mention trinomials but you can use the same method for them.
  Button navigates to signup page
  (1 vote)
Sindisiwe Yolanda
Posted 4 years ago. Direct link to Sindisiwe Yolanda's post “Is this method the same o...”
Is this method the same one as the foil one?
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(1 vote)
Answer
- shreyas.param
  Posted 4 years ago. Direct link to shreyas.param's post “The method is same as foi...”
  The method is same as foil but the better method is the method said by Sal
  Button navigates to signup page
  (2 votes)
dmonte scott
Posted 5 years ago. Direct link to dmonte scott's post “how is this going to help...”
how is this going to help me count my money or get a job
Button navigates to signup pageButton navigates to signup page
(1 vote)
Answer
- David Severin
  Posted 5 years ago. Direct link to David Severin's post “That depends on what job ...”
  That depends on what job you have - most majors in college require some math to graduate, so counting money as a burger flipper is easier than as an engineer because there is so much less to count. Even doctors and lawyers who have a lot of money to count must take math to get to where they are.
  Button navigates to signup page
  (2 votes)
Ash
Posted 3 years ago. Direct link to Ash's post “How do you visualize (x-4...”
How do you visualize (x-4)(x+7) as an area? I tried it with one side of the area marked as x-4 + (4) and the other as x + 7 but couldn't get the correct answer.
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(2 votes)
Answer
- lugumedeiros
  Posted 14 days ago. Direct link to lugumedeiros's post “+ --- (x-4) --- + | | (x+...”
  + --- (x-4) --- +
  |
  |
  (x+7)
  |
  |
  + --- (x-4) --- +
  
  better later than never I guess...
  Button navigates to signup page
  (0 votes)
Jarl Riskjell Gjerde
Posted 5 years ago. Direct link to Jarl Riskjell Gjerde's post “Is it called Standard Qua...”
Is it called Standard Quadratic Form because it can be expressed as a sum of squares and rectangles?
Why do we call expressions of the form (x+y)(p-q), (x+y)(p+q), etc. for standard quadratic forms?
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(1 vote)
Answer
- Singh
  Posted 5 years ago. Direct link to Singh's post “Standard Quadratic Form i...”
  Standard Quadratic Form is in the form of y=ax^2+bx+c and its not because it is the sum of squares and rectangles (that is just how it could be applied).
  
  Those expressions are in the form for standard quadratic forms because once they are multiplied they would be in the form of ax^2+bx+c (assuming p and q are constants).
  Button navigates to signup page
  (1 vote)