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Multiplying Binomials (Special Cases)

In this video, we are going to look at how to multiply special cases of binomials.

For example:
To multiply (x+b)^2 we have to multiply the binomial by itself. When we foil it, we get
x^2+bx+bx+b^2
After combining like terms, this simplifies to
x^2+2bx+b^2
By following this form, we can use this to solve any squared binomial.
For example:
(x+4)^2
can be solved by plugging in 4 for where we see b. This will give us a final answer of
x^2+8x+16
Another special case example would be to multiply (x+b)(x-b)
When we foil it we get
x^2-bx+bx-b^2
After combining like terms, it simplifies to
x^2-b^2
By following this form, we can use this to solve other binomials written this way.
For example:
(x+4)(x-4)
would be easily solvable by plugging in 4 for where we see b. This will give us a final answer of
x^2-16

Video-Lesson Transcript

Let’s go over multiplying binomials with special cases.

For example:

(x + b)^2

This is multiplying a binomial by itself.

So what happens is this

(x + b) (x + b)
x^2 + bx + bx + b^2
x^2 + 2bx + b^2

This means that you can immediately get the product of these two binomials if you follow this format.

For example:

(x + 4)^2
(x + b)^2 = x^2 + 8x + 16

I’ll do the math and check if that’s true.

(x + 4) (x + 4)
x^2 + 4x + 4x + 16

Combine like terms

x^2 + 8x + 16

So, it’s supposed to come out like this.

Let’s have another special case.

(x + b) (x - b)
x^2 - bx + bx - b^2

So if we combine like terms, we’ll have

x^2 - b^2

So if we have

(x + 4) (x - 4)
x^2 - 16

If we multiply it, we’ll have the same thing

(x + 4) (x - 4)
x^2 - 4x + 4x - 16
x^2 - 16

Just like what we got earlier.

So in these special cases, just follow the format that we have above.