How can you tell if a binomial is a difference of two perfect squares and how does the process of factoring a difference of two perfect squares?

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A binomial of difference of two squares has a form:

`a^2 - b^2`

From its name difference of two squares, the operation between the two terms a^2 and b^2 is subtraction.

And its factor form is:

`a^2 - b^2=(a-b)(a+b)`

For example:

`x^2 - 9`

This is a binomial of difference...

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A binomial of difference of two squares has a form:

`a^2 - b^2`

From its name difference of two squares, the operation between the two terms a^2 and b^2 is subtraction.

And its factor form is:

`a^2 - b^2=(a-b)(a+b)`

For example:

`x^2 - 9`

This is a binomial of difference of two squares because:

(1) the first term is in the form a^2,

(2) the second term can be express as b^2, since 9=3^2, and

(3) the operation between the two terms is subtraction.

So, the given binomial can be re-written as:

`=x^2-3^2`

Now that it is the form a^2 - b^2, apply its factor (a-b)(a+b).

`=(x-3)(x+3)`

Hence,  `x^2-9=(x-3)(x+3).`

 

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