Basic Math Examples

$w (w + 1) (w + 2) = 40$

Step 1

Simplify $w (w + 1) (w + 2)$ .

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Step 1.1

Simplify by multiplying through.

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Step 1.1.1

Apply the distributive property.

$(w \cdot w + w \cdot 1) (w + 2) = 40$

Step 1.1.2

Simplify the expression.

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Step 1.1.2.1

Multiply $w$ by $w$ .

$(w^{2} + w \cdot 1) (w + 2) = 40$

Step 1.1.2.2

Multiply $w$ by $1$ .

$(w^{2} + w) (w + 2) = 40$

Step 1.2

Expand $(w^{2} + w) (w + 2)$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

$w^{2} (w + 2) + w (w + 2) = 40$

Step 1.2.2

Apply the distributive property.

$w^{2} w + w^{2} \cdot 2 + w (w + 2) = 40$

Step 1.2.3

Apply the distributive property.

$w^{2} w + w^{2} \cdot 2 + w \cdot w + w \cdot 2 = 40$

Step 1.3

Simplify and combine like terms.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

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

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Step 1.3.1.1.1

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

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Step 1.3.1.1.1.1

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

$w^{2} w^{1} + w^{2} \cdot 2 + w \cdot w + w \cdot 2 = 40$

Step 1.3.1.1.1.2

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

$w^{2 + 1} + w^{2} \cdot 2 + w \cdot w + w \cdot 2 = 40$

Step 1.3.1.1.2

Add $2$ and $1$ .

$w^{3} + w^{2} \cdot 2 + w \cdot w + w \cdot 2 = 40$

Step 1.3.1.2

Move $2$ to the left of $w^{2}$ .

$w^{3} + 2 \cdot w^{2} + w \cdot w + w \cdot 2 = 40$

Step 1.3.1.3

Multiply $w$ by $w$ .

$w^{3} + 2 w^{2} + w^{2} + w \cdot 2 = 40$

Step 1.3.1.4

Move $2$ to the left of $w$ .

$w^{3} + 2 w^{2} + w^{2} + 2 w = 40$

Step 1.3.2

Add $2 w^{2}$ and $w^{2}$ .

$w^{3} + 3 w^{2} + 2 w = 40$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$w \approx 2.51739351$

Step 3