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## Algebra basics

### Course: Algebra basics>Unit 7

Lesson 2: 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 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?
(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)
• how do I put the answer in the text box it wont let me.
(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
(1 vote)
• So what would be the actual definition for 'expanding brackets' or 'binomial products'? I'm doing a TTL, and I need the definitions. Thxs!
(1 vote)