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## College Algebra

### Course: College Algebra > Unit 4

Lesson 2: Special products of binomials- Special products of the form (x+a)(x-a)
- Squaring binomials of the form (x+a)²
- Multiply difference of squares
- Multiply perfect squares of binomials
- Special products of the form (ax+b)(ax-b)
- Squaring binomials of the form (ax+b)²
- Binomial special products review

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# Binomial special products review

A review of the difference of squares pattern (a+b)(a-b)=a^2-b^2, as well as other common patterns encountered while multiplying binomials, such as (a+b)^2=a^2+2ab+b^2.

These types of binomial multiplication problems come up time and time again, so it's good to be familiar with some basic patterns.

The "difference of squares" pattern:

Two other patterns:

### Example 1

**Expand the expression.**

The expression fits the difference of squares pattern:

So our answer is:

But if you don't recognize the pattern, that's okay too. Just multiply the binomials as normal. Over time, you'll learn to see the pattern.

Notice how the "middle terms" cancel.

*Want another example? Check out this video.*

### Example 2

**Expand the expression.**

The expression fits this pattern:

So our answer is:

But if you don't recognize the pattern, that's okay too. Just multiply the binomials as normal. Over time, you'll learn to see the pattern.

*Want another example? Check out this video.*

### Example 3

**Expand this expression.**

The expression fits the difference of squares pattern:

So our answer is:

But if you don't recognize the pattern, that's okay too. Just multiply the binomials as normal. Over time, you'll learn to see the pattern.

Notice how the "middle terms" cancel.

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

## Want to join the conversation?

- What's the point of memorizing these patterns? I think it's better just to solve the problems instead of memorizing some sort of pattern.(30 votes)
- For multiplication, you're right... it can be just as easy to just multiply the binomials like any other binomials. However, learning the patterns will help you later when you learn how to:

1) Factor polynomials

2) Solve quadratic equations by completing the square

3) Completing the square to work with equations for circles(64 votes)

- How would I cube a polynomial?(15 votes)
- square it first, then multiply the square times the polynomial, it could get complicated, but doable(15 votes)

- I'm studying for my teacher certification, and just went through as many videos on polynomials as I could. On my practice test, there was a problem I hope to get explained. It read "(3+2i)(4+3i)" and the answer was "6+17i". How did the 6i^2 end up cancelled out and subtracting 6 as well? Very confused. Does it matter if the letters are after the constants in the problem?(9 votes)
- Remember, i = sqrt(-1)

i^2 = sqrt(-1) * sqrt(-1) = -1

Thus, 6i^2 = 6(-1) = -6

Hope this helps.(17 votes)

- why do we need this if we forget it when we are in our 40s(4 votes)
- I am in my 60s and I still remember it, if you do not put any value on what you are learning, you may forget it in your 20s.(23 votes)

- if you solve enough of these, the answers start to jump out. The advantage is that you'll then have a pattern of understanding that will make future lessons easier.(11 votes)
- What would you do if you were trying to do (8x-5)^5 and your calculator says: Overflow Error(5 votes)
- x can be any number, so the calculator doesn't know which number equals x, so x can be any number, so then the equation then can equal anything.

If you wanted to put it in standard form, you would:

see below.↓.Hope this helps.(6 votes)

- what is the best way to remember how to add and subtract or multiple and divide negatives(5 votes)
- Like everything else in mathematics, the key is practice. Instead of just memorizing the formula, if you solve enough of these, the answers start to jump out. The advantage is that you'll then have a pattern of understanding that will make future lessons easier.(3 votes)

- I cant see the patterns! The only way I can solve these is by using the distributive property. Anyone else have this issue?(3 votes)
- It will come with time as you continue to solve them by using the distributive property. When it does, you will just be able to solve them a little more quickly.(6 votes)

- Can't you just use the are model and get the same answer?(4 votes)
- Why is (a+b)^2 quadratics form if this is polynomials?(2 votes)