Calculus Examples

$x (90 - x) (60 - 2 x)$

Step 1

Simplify terms.

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Step 1.1

Apply the distributive property.

$(x \cdot 90 + x (- x)) (60 - 2 x)$

Step 1.2

Reorder.

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Step 1.2.1

Move $90$ to the left of $x$ .

$(90 \cdot x + x (- x)) (60 - 2 x)$

Step 1.2.2

Rewrite using the commutative property of multiplication.

$(90 \cdot x - x \cdot x) (60 - 2 x)$

Step 1.3

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

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Step 1.3.1

Move $x$ .

$(90 x - (x \cdot x)) (60 - 2 x)$

Step 1.3.2

Multiply $x$ by $x$ .

$(90 x - x^{2}) (60 - 2 x)$

Step 2

Expand $(90 x - x^{2}) (60 - 2 x)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$90 x (60 - 2 x) - x^{2} (60 - 2 x)$

Step 2.2

Apply the distributive property.

$90 x \cdot 60 + 90 x (- 2 x) - x^{2} (60 - 2 x)$

Step 2.3

Apply the distributive property.

$90 x \cdot 60 + 90 x (- 2 x) - x^{2} \cdot 60 - x^{2} (- 2 x)$

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $60$ by $90$ .

$5400 x + 90 x (- 2 x) - x^{2} \cdot 60 - x^{2} (- 2 x)$

Step 3.1.2

Rewrite using the commutative property of multiplication.

$5400 x + 90 \cdot - 2 x \cdot x - x^{2} \cdot 60 - x^{2} (- 2 x)$

Step 3.1.3

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

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Step 3.1.3.1

Move $x$ .

$5400 x + 90 \cdot - 2 (x \cdot x) - x^{2} \cdot 60 - x^{2} (- 2 x)$

Step 3.1.3.2

Multiply $x$ by $x$ .

$5400 x + 90 \cdot - 2 x^{2} - x^{2} \cdot 60 - x^{2} (- 2 x)$

Step 3.1.4

Multiply $90$ by $- 2$ .

$5400 x - 180 x^{2} - x^{2} \cdot 60 - x^{2} (- 2 x)$

Step 3.1.5

Multiply $60$ by $- 1$ .

$5400 x - 180 x^{2} - 60 x^{2} - x^{2} (- 2 x)$

Step 3.1.6

Rewrite using the commutative property of multiplication.

$5400 x - 180 x^{2} - 60 x^{2} - 1 \cdot - 2 x^{2} x$

Step 3.1.7

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

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Step 3.1.7.1

Move $x$ .

$5400 x - 180 x^{2} - 60 x^{2} - 1 \cdot - 2 (x \cdot x^{2})$

Step 3.1.7.2

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

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Step 3.1.7.2.1

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

$5400 x - 180 x^{2} - 60 x^{2} - 1 \cdot - 2 (x^{1} x^{2})$

Step 3.1.7.2.2

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

$5400 x - 180 x^{2} - 60 x^{2} - 1 \cdot - 2 x^{1 + 2}$

Step 3.1.7.3

Add $1$ and $2$ .

$5400 x - 180 x^{2} - 60 x^{2} - 1 \cdot - 2 x^{3}$

Step 3.1.8

Multiply $- 1$ by $- 2$ .

$5400 x - 180 x^{2} - 60 x^{2} + 2 x^{3}$

Step 3.2

Subtract $60 x^{2}$ from $- 180 x^{2}$ .

$5400 x - 240 x^{2} + 2 x^{3}$