Calculus Examples

$5 x {(x + 4)}^{3}$

Step 1

Use the Binomial Theorem.

$5 x (x^{3} + 3 x^{2} \cdot 4 + 3 x \cdot 4^{2} + 4^{3})$

Step 2

Simplify terms.

Tap for more steps...

Step 2.1

Simplify each term.

Tap for more steps...

Step 2.1.1

Multiply $4$ by $3$ .

$5 x (x^{3} + 12 x^{2} + 3 x \cdot 4^{2} + 4^{3})$

Step 2.1.2

Raise $4$ to the power of $2$ .

$5 x (x^{3} + 12 x^{2} + 3 x \cdot 16 + 4^{3})$

Step 2.1.3

Multiply $16$ by $3$ .

$5 x (x^{3} + 12 x^{2} + 48 x + 4^{3})$

Step 2.1.4

Raise $4$ to the power of $3$ .

$5 x (x^{3} + 12 x^{2} + 48 x + 64)$

Step 2.2

Apply the distributive property.

$5 x \cdot x^{3} + 5 x (12 x^{2}) + 5 x (48 x) + 5 x \cdot 64$

Step 3

Simplify.

Tap for more steps...

Step 3.1

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

Tap for more steps...

Step 3.1.1

Move $x^{3}$ .

$5 (x^{3} x) + 5 x (12 x^{2}) + 5 x (48 x) + 5 x \cdot 64$

Step 3.1.2

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

Tap for more steps...

Step 3.1.2.1

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

$5 (x^{3} x^{1}) + 5 x (12 x^{2}) + 5 x (48 x) + 5 x \cdot 64$

Step 3.1.2.2

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

$5 x^{3 + 1} + 5 x (12 x^{2}) + 5 x (48 x) + 5 x \cdot 64$

Step 3.1.3

Add $3$ and $1$ .

$5 x^{4} + 5 x (12 x^{2}) + 5 x (48 x) + 5 x \cdot 64$

Step 3.2

Rewrite using the commutative property of multiplication.

$5 x^{4} + 5 \cdot 12 x \cdot x^{2} + 5 x (48 x) + 5 x \cdot 64$

Step 3.3

Rewrite using the commutative property of multiplication.

$5 x^{4} + 5 \cdot 12 x \cdot x^{2} + 5 \cdot 48 x \cdot x + 5 x \cdot 64$

Step 3.4

Multiply $64$ by $5$ .

$5 x^{4} + 5 \cdot 12 x \cdot x^{2} + 5 \cdot 48 x \cdot x + 320 x$

Step 4

Simplify each term.

Tap for more steps...

Step 4.1

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

Tap for more steps...

Step 4.1.1

Move $x^{2}$ .

$5 x^{4} + 5 \cdot 12 (x^{2} x) + 5 \cdot 48 x \cdot x + 320 x$

Step 4.1.2

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

Tap for more steps...

Step 4.1.2.1

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

$5 x^{4} + 5 \cdot 12 (x^{2} x^{1}) + 5 \cdot 48 x \cdot x + 320 x$

Step 4.1.2.2

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

$5 x^{4} + 5 \cdot 12 x^{2 + 1} + 5 \cdot 48 x \cdot x + 320 x$

Step 4.1.3

Add $2$ and $1$ .

$5 x^{4} + 5 \cdot 12 x^{3} + 5 \cdot 48 x \cdot x + 320 x$

Step 4.2

Multiply $5$ by $12$ .

$5 x^{4} + 60 x^{3} + 5 \cdot 48 x \cdot x + 320 x$

Step 4.3

Multiply $x$ by $x$ by adding the exponents.

Tap for more steps...

Step 4.3.1

Move $x$ .

$5 x^{4} + 60 x^{3} + 5 \cdot 48 (x \cdot x) + 320 x$

Step 4.3.2

Multiply $x$ by $x$ .

$5 x^{4} + 60 x^{3} + 5 \cdot 48 x^{2} + 320 x$

Step 4.4

Multiply $5$ by $48$ .

$5 x^{4} + 60 x^{3} + 240 x^{2} + 320 x$