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Algebra basics
Course: Algebra basics > Unit 7
Lesson 2: Multiplying binomials Multiplying monomials by polynomials
 Multiply monomials by polynomials
 Multiplying monomials by polynomials review
 Multiplying binomials: area model
 Multiplying binomials intro
 Multiply binomials intro
 Multiplying binomials
 Multiply binomials
 Multiplying binomials review
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Multiplying binomials review
A binomial is a polynomial with two terms. For example, $x2$ and $x6$ are both binomials. In this article, we'll review how to multiply these binomials.
Example 1
Expand the expression.
Apply the distributive property.
Apply the distributive property again.
Notice the pattern. We multiplied each term in the first binomial by each term in the second binomial.
Simplify.
Example 2
Expand the expression.
Apply the distributive property.
Apply the distributive property again.
Notice the pattern. We multiplied each term in the first binomial by each term in the second binomial.
Simplify:
Want to learn more about multiplying binomials? Check out this video.
Want to join the conversation?
 Is it okay if I use this method? :
(9h+3)(h1)
h(9h+3)1(9h+3)
9h^23h9h3
9h^212h3
This is what Sal showed in the multiplying binomials video.(9 votes) 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(h1) + 3(h1), just that on your 3rd step, the 9h and 3h would be interchanged.(9 votes)
 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??(10 votes)
 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.(6 votes)
 whats bigger than a quadratic equation?(3 votes)
 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.(5 votes)
 For those interested, Q2 can be simplified further (although the question doesn't want it).
(6d+6)(2d2)
= 6(d1)x2(d1)
= 12(d1)(d1)
= 12(d1)^2(4 votes)  (4ab+2) (3ab7)?(3 votes)
 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/introductiontopolynomialexpressions/multiplyingbinomials2/v/multiplyingbinomials
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.(2 votes)
 Does this mention trinomials(1 vote)
 It does not mention trinomials but you can use the same method for them.(1 vote)
 Is this method the same one as the foil one?(1 vote)
 The method is same as foil but the better method is the method said by Sal(2 votes)
 how is this going to help me count my money or get a job(1 vote)
 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.(2 votes)
 How do you visualize (x4)(x+7) as an area? I tried it with one side of the area marked as x4 + (4) and the other as x + 7 but couldn't get the correct answer.(2 votes)
 +  (x4)  +


(x+7)


+  (x4)  +
better later than never I guess...(0 votes)
 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)(pq), (x+y)(p+q), etc. for standard quadratic forms?(1 vote) 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).(1 vote)