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

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

Step 1

Apply the distributive property.

$(4 x^{2} x + 4 x^{2} \cdot - 2) (x + 2)$

Step 2

Multiply $x^{2}$ by $x$ by adding the exponents.

Move $x$ .

$(4 (x \cdot x^{2}) + 4 x^{2} \cdot - 2) (x + 2)$

Multiply $x$ by $x^{2}$ .

Raise $x$ to the power of $1$ .

$(4 (x^{1} x^{2}) + 4 x^{2} \cdot - 2) (x + 2)$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$(4 x^{1 + 2} + 4 x^{2} \cdot - 2) (x + 2)$

Add $1$ and $2$ .

$(4 x^{3} + 4 x^{2} \cdot - 2) (x + 2)$

Step 3

Multiply $- 2$ by $4$ .

$(4 x^{3} - 8 x^{2}) (x + 2)$

Step 4

Expand $(4 x^{3} - 8 x^{2}) (x + 2)$ using the FOIL Method.

Apply the distributive property.

$4 x^{3} (x + 2) - 8 x^{2} (x + 2)$

Apply the distributive property.

$4 x^{3} x + 4 x^{3} \cdot 2 - 8 x^{2} (x + 2)$

Apply the distributive property.

$4 x^{3} x + 4 x^{3} \cdot 2 - 8 x^{2} x - 8 x^{2} \cdot 2$

Step 5

Simplify and combine like terms.

Simplify each term.

Multiply $x^{3}$ by $x$ by adding the exponents.

Move $x$ .

$4 (x \cdot x^{3}) + 4 x^{3} \cdot 2 - 8 x^{2} x - 8 x^{2} \cdot 2$

Multiply $x$ by $x^{3}$ .

Raise $x$ to the power of $1$ .

$4 (x^{1} x^{3}) + 4 x^{3} \cdot 2 - 8 x^{2} x - 8 x^{2} \cdot 2$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$4 x^{1 + 3} + 4 x^{3} \cdot 2 - 8 x^{2} x - 8 x^{2} \cdot 2$

Add $1$ and $3$ .

$4 x^{4} + 4 x^{3} \cdot 2 - 8 x^{2} x - 8 x^{2} \cdot 2$

Multiply $2$ by $4$ .

$4 x^{4} + 8 x^{3} - 8 x^{2} x - 8 x^{2} \cdot 2$

Multiply $x^{2}$ by $x$ by adding the exponents.

Move $x$ .

$4 x^{4} + 8 x^{3} - 8 (x \cdot x^{2}) - 8 x^{2} \cdot 2$

Multiply $x$ by $x^{2}$ .

Raise $x$ to the power of $1$ .

$4 x^{4} + 8 x^{3} - 8 (x^{1} x^{2}) - 8 x^{2} \cdot 2$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$4 x^{4} + 8 x^{3} - 8 x^{1 + 2} - 8 x^{2} \cdot 2$

Add $1$ and $2$ .

$4 x^{4} + 8 x^{3} - 8 x^{3} - 8 x^{2} \cdot 2$

Multiply $2$ by $- 8$ .

$4 x^{4} + 8 x^{3} - 8 x^{3} - 16 x^{2}$

Subtract $8 x^{3}$ from $8 x^{3}$ .

$4 x^{4} + 0 - 16 x^{2}$

Add $4 x^{4}$ and $0$ .

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

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

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