Main content

## Algebra (all content)

### Unit 10: Lesson 7

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
- Special products of the form (ax+b)(ax-b)
- Squaring binomials of the form (ax+b)²
- Special products of binomials: two variables
- More examples of special products
- Polynomial special products: perfect square
- Squaring a binomial (old)
- Binomial special products review

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# Binomial special products review

CCSS.Math:

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.(17 votes)
- If you consider
**why**these patterns are true (for example by going through the process of multiplying out the binomials in each pattern), then you will have an easier time remembering them.

The following videos of geometric area models can also help you remember these patterns.

https://m.youtube.com/watch?v=KaEBWPBugG4

https://m.youtube.com/watch?v=24gWbMSEVVw(3 votes)

- How would I cube a polynomial?(13 votes)
- square it first, then multiply the square times the polynomial, it could get complicated, but doable(12 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.(10 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?(8 votes)
- Remember, i = sqrt(-1)

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

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

Hope this helps.(3 votes)

- What would you do if you were trying to do (8x-5)^5 and your calculator says: Overflow Error(4 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.(5 votes)

- what is the best way to remember how to add and subtract or multiple and divide negatives(4 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.(2 votes)

- Can't you just use the are model and get the same answer?(3 votes)
- Why is (a+b)^2 quadratics form if this is polynomials?(1 vote)
- why do we need this if we forget it when we are in our 40s(2 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.(2 votes)

- If we have (x-10)(x+10), then we can just cancel out (-10+10)x to leave us with x^2 + (-10*10) right?(1 vote)
- That is correct, thus ending up with x^2 - 100 which is called the difference (subtract) of perfect squares.(3 votes)