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## Algebra (all content)

### Course: Algebra (all content)>Unit 10

Lesson 6: Multiplying binomials

# Multiplying binomials review

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

## Practice

Problem 1
• Current
Simplify.
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?

• 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.
• 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.
• 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.
• 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
• (4ab+2) (3ab-7)?
• 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
• 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.
• 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.
• + --- (x-4) --- +
|
|
(x+7)
|
|
+ --- (x-4) --- +

better later than never I guess...