Basic Math Examples

$5 w (w^{2} - 7 w y + 3 y) + 2 w (2 y + 19 w y - 2 w^{2})$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$5 w \cdot w^{2} + 5 w (- 7 w y) + 5 w (3 y) + 2 w (2 y + 19 w y - 2 w^{2})$

Step 1.2

Simplify.

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Step 1.2.1

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

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Step 1.2.1.1

Move $w^{2}$ .

$5 (w^{2} w) + 5 w (- 7 w y) + 5 w (3 y) + 2 w (2 y + 19 w y - 2 w^{2})$

Step 1.2.1.2

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

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Step 1.2.1.2.1

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

$5 (w^{2} w^{1}) + 5 w (- 7 w y) + 5 w (3 y) + 2 w (2 y + 19 w y - 2 w^{2})$

Step 1.2.1.2.2

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

$5 w^{2 + 1} + 5 w (- 7 w y) + 5 w (3 y) + 2 w (2 y + 19 w y - 2 w^{2})$

Step 1.2.1.3

Add $2$ and $1$ .

$5 w^{3} + 5 w (- 7 w y) + 5 w (3 y) + 2 w (2 y + 19 w y - 2 w^{2})$

Step 1.2.2

Multiply $w$ by $w$ by adding the exponents.

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Step 1.2.2.1

Move $w$ .

$5 w^{3} + 5 (w \cdot w) (- 7 y) + 5 w (3 y) + 2 w (2 y + 19 w y - 2 w^{2})$

Step 1.2.2.2

Multiply $w$ by $w$ .

$5 w^{3} + 5 w^{2} (- 7 y) + 5 w (3 y) + 2 w (2 y + 19 w y - 2 w^{2})$

Step 1.2.3

Rewrite using the commutative property of multiplication.

$5 w^{3} + 5 w^{2} (- 7 y) + 5 \cdot 3 w y + 2 w (2 y + 19 w y - 2 w^{2})$

Step 1.3

Simplify each term.

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Step 1.3.1

Rewrite using the commutative property of multiplication.

$5 w^{3} + 5 \cdot - 7 w^{2} y + 5 \cdot 3 w y + 2 w (2 y + 19 w y - 2 w^{2})$

Step 1.3.2

Multiply $5$ by $- 7$ .

$5 w^{3} - 35 w^{2} y + 5 \cdot 3 w y + 2 w (2 y + 19 w y - 2 w^{2})$

Step 1.3.3

Multiply $5$ by $3$ .

$5 w^{3} - 35 w^{2} y + 15 w y + 2 w (2 y + 19 w y - 2 w^{2})$

Step 1.4

Apply the distributive property.

$5 w^{3} - 35 w^{2} y + 15 w y + 2 w (2 y) + 2 w (19 w y) + 2 w (- 2 w^{2})$

Step 1.5

Simplify.

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Step 1.5.1

Rewrite using the commutative property of multiplication.

$5 w^{3} - 35 w^{2} y + 15 w y + 2 \cdot 2 w y + 2 w (19 w y) + 2 w (- 2 w^{2})$

Step 1.5.2

Multiply $w$ by $w$ by adding the exponents.

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Step 1.5.2.1

Move $w$ .

$5 w^{3} - 35 w^{2} y + 15 w y + 2 \cdot 2 w y + 2 (w \cdot w) (19 y) + 2 w (- 2 w^{2})$

Step 1.5.2.2

Multiply $w$ by $w$ .

$5 w^{3} - 35 w^{2} y + 15 w y + 2 \cdot 2 w y + 2 w^{2} (19 y) + 2 w (- 2 w^{2})$

Step 1.5.3

Rewrite using the commutative property of multiplication.

$5 w^{3} - 35 w^{2} y + 15 w y + 2 \cdot 2 w y + 2 w^{2} (19 y) + 2 \cdot - 2 w \cdot w^{2}$

Step 1.6

Simplify each term.

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Step 1.6.1

Multiply $2$ by $2$ .

$5 w^{3} - 35 w^{2} y + 15 w y + 4 w y + 2 w^{2} (19 y) + 2 \cdot - 2 w \cdot w^{2}$

Step 1.6.2

Rewrite using the commutative property of multiplication.

$5 w^{3} - 35 w^{2} y + 15 w y + 4 w y + 2 \cdot 19 w^{2} y + 2 \cdot - 2 w \cdot w^{2}$

Step 1.6.3

Multiply $2$ by $19$ .

$5 w^{3} - 35 w^{2} y + 15 w y + 4 w y + 38 w^{2} y + 2 \cdot - 2 w \cdot w^{2}$

Step 1.6.4

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

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Step 1.6.4.1

Move $w^{2}$ .

$5 w^{3} - 35 w^{2} y + 15 w y + 4 w y + 38 w^{2} y + 2 \cdot - 2 (w^{2} w)$

Step 1.6.4.2

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

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Step 1.6.4.2.1

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

$5 w^{3} - 35 w^{2} y + 15 w y + 4 w y + 38 w^{2} y + 2 \cdot - 2 (w^{2} w^{1})$

Step 1.6.4.2.2

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

$5 w^{3} - 35 w^{2} y + 15 w y + 4 w y + 38 w^{2} y + 2 \cdot - 2 w^{2 + 1}$

Step 1.6.4.3

Add $2$ and $1$ .

$5 w^{3} - 35 w^{2} y + 15 w y + 4 w y + 38 w^{2} y + 2 \cdot - 2 w^{3}$

Step 1.6.5

Multiply $2$ by $- 2$ .

$5 w^{3} - 35 w^{2} y + 15 w y + 4 w y + 38 w^{2} y - 4 w^{3}$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $4 w^{3}$ from $5 w^{3}$ .

$w^{3} - 35 w^{2} y + 15 w y + 4 w y + 38 w^{2} y$

Step 2.2

Add $- 35 w^{2} y$ and $38 w^{2} y$ .

$w^{3} + 3 w^{2} y + 15 w y + 4 w y$

Step 2.3

Add $15 w y$ and $4 w y$ .

$w^{3} + 3 w^{2} y + 19 w y$