$4{x}^{2}-16$

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Find the Greatest Common Factor (GCF).

What is the largest number that divides evenly into

4{x}^{2}

and

-16

It is

4

What is the highest degree of $x$ that divides evenly into

4{x}^{2}

and

-16

It is 1, since

x

is not in every term.

Multiplying the results above,

The GCF is

4

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GCF =

4

Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)

4(\frac{4{x}^{2}}{4}-\frac{16}{4})

Simplify each term in parentheses.

4({x}^{2}-4)

Rewrite

{x}^{2}-4

in the form

{a}^{2}-{b}^{2}

, where

a=x

and

b=2

4({x}^{2}-{2}^{2})

Use Difference of Squares:

{a}^{2}-{b}^{2}=(a+b)(a-b)

4(x+2)(x-2)

Done

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4x2−164{x}^{2}-164x2−16