Calculus Examples

$x {(x - 15)}^{2}$

Step 1

Rewrite ${(x - 15)}^{2}$ as $(x - 15) (x - 15)$ .

$x ((x - 15) (x - 15))$

Step 2

Expand $(x - 15) (x - 15)$ using the FOIL Method.

Tap for more steps...

Step 2.1

Apply the distributive property.

$x (x (x - 15) - 15 (x - 15))$

Step 2.2

Apply the distributive property.

$x (x \cdot x + x \cdot - 15 - 15 (x - 15))$

Step 2.3

Apply the distributive property.

$x (x \cdot x + x \cdot - 15 - 15 x - 15 \cdot - 15)$

Step 3

Simplify and combine like terms.

Tap for more steps...

Step 3.1

Simplify each term.

Tap for more steps...

Step 3.1.1

Multiply $x$ by $x$ .

$x (x^{2} + x \cdot - 15 - 15 x - 15 \cdot - 15)$

Step 3.1.2

Move $- 15$ to the left of $x$ .

$x (x^{2} - 15 \cdot x - 15 x - 15 \cdot - 15)$

Step 3.1.3

Multiply $- 15$ by $- 15$ .

$x (x^{2} - 15 x - 15 x + 225)$

Step 3.2

Subtract $15 x$ from $- 15 x$ .

$x (x^{2} - 30 x + 225)$

Step 4

Apply the distributive property.

$x \cdot x^{2} + x (- 30 x) + x \cdot 225$

Step 5

Simplify.

Tap for more steps...

Step 5.1

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

Tap for more steps...

Step 5.1.1

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

Tap for more steps...

Step 5.1.1.1

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

$x^{1} x^{2} + x (- 30 x) + x \cdot 225$

Step 5.1.1.2

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

$x^{1 + 2} + x (- 30 x) + x \cdot 225$

Step 5.1.2

Add $1$ and $2$ .

$x^{3} + x (- 30 x) + x \cdot 225$

Step 5.2

Rewrite using the commutative property of multiplication.

$x^{3} - 30 x \cdot x + x \cdot 225$

Step 5.3

Move $225$ to the left of $x$ .

$x^{3} - 30 x \cdot x + 225 \cdot x$

Step 6

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

Tap for more steps...

Step 6.1

Move $x$ .

$x^{3} - 30 (x \cdot x) + 225 \cdot x$

Step 6.2

Multiply $x$ by $x$ .

$x^{3} - 30 x^{2} + 225 \cdot x$

$x^{3} - 30 x^{2} + 225 x$