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### Course: Algebra basics>Unit 7

Lesson 2: Multiplying binomials

# Multiplying binomials review

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

### Example 1

Expand the expression.
$\left(x-2\right)\left(x-6\right)$
Apply the distributive property.
$\begin{array}{rl}& \left(x-2\right)\left(x-6\right)\\ \\ =& x\left(x-6\right)-2\left(x-6\right)\end{array}$
Apply the distributive property again.
$=x\left(x\right)+x\left(-6\right)-2\left(x\right)-2\left(-6\right)$
Notice the pattern. We multiplied each term in the first binomial by each term in the second binomial.
Simplify.
$\begin{array}{rl}=& {x}^{2}-6x-2x+12\\ \\ =& {x}^{2}-8x+12\end{array}$

### Example 2

Expand the expression.
$\left(-a+1\right)\left(5a+6\right)$
Apply the distributive property.
$\begin{array}{rl}& \left(-a+1\right)\left(5a+6\right)\\ \\ =& -a\left(5a+6\right)+1\left(5a+6\right)\end{array}$
Apply the distributive property again.
$=-a\left(5a\right)-a\left(6\right)+1\left(5a\right)+1\left(6\right)$
Notice the pattern. We multiplied each term in the first binomial by each term in the second binomial.
Simplify:
$-5{a}^{2}-a+6$

## Practice

Problem 1
Simplify.
$\left(x+1\right)\left(x-6\right)$

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.
• (4ab+2) (3ab-7)?
• 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
• Does this mention trinomials
(1 vote)
• It does not mention trinomials but you can use the same method for them.
(1 vote)
• So what exactly does this help us with in real life? Does help figure out like finances or a building or something.
(1 vote)
• 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.