Algebra Examples

$- 5 w^{2} (8 w^{2} x - 11 w x^{2}) + 6 x (9 w x^{4} - 4 w - 3 x^{2})$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$- 5 w^{2} (8 w^{2} x) - 5 w^{2} (- 11 w x^{2}) + 6 x (9 w x^{4} - 4 w - 3 x^{2})$

Step 1.2

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

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Step 1.2.1

Move $w^{2}$ .

$- 5 (w^{2} w^{2}) (8 x) - 5 w^{2} (- 11 w x^{2}) + 6 x (9 w x^{4} - 4 w - 3 x^{2})$

Step 1.2.2

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

$- 5 w^{2 + 2} (8 x) - 5 w^{2} (- 11 w x^{2}) + 6 x (9 w x^{4} - 4 w - 3 x^{2})$

Step 1.2.3

Add $2$ and $2$ .

$- 5 w^{4} (8 x) - 5 w^{2} (- 11 w x^{2}) + 6 x (9 w x^{4} - 4 w - 3 x^{2})$

Step 1.3

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

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Step 1.3.1

Move $w$ .

$- 5 w^{4} (8 x) - 5 (w \cdot w^{2}) (- 11 x^{2}) + 6 x (9 w x^{4} - 4 w - 3 x^{2})$

Step 1.3.2

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

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Step 1.3.2.1

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

$- 5 w^{4} (8 x) - 5 (w^{1} w^{2}) (- 11 x^{2}) + 6 x (9 w x^{4} - 4 w - 3 x^{2})$

Step 1.3.2.2

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

$- 5 w^{4} (8 x) - 5 w^{1 + 2} (- 11 x^{2}) + 6 x (9 w x^{4} - 4 w - 3 x^{2})$

Step 1.3.3

Add $1$ and $2$ .

$- 5 w^{4} (8 x) - 5 w^{3} (- 11 x^{2}) + 6 x (9 w x^{4} - 4 w - 3 x^{2})$

Step 1.4

Simplify each term.

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Step 1.4.1

Rewrite using the commutative property of multiplication.

$- 5 \cdot 8 w^{4} x - 5 w^{3} (- 11 x^{2}) + 6 x (9 w x^{4} - 4 w - 3 x^{2})$

Step 1.4.2

Multiply $- 5$ by $8$ .

$- 40 w^{4} x - 5 w^{3} (- 11 x^{2}) + 6 x (9 w x^{4} - 4 w - 3 x^{2})$

Step 1.4.3

Rewrite using the commutative property of multiplication.

$- 40 w^{4} x - 5 \cdot - 11 w^{3} x^{2} + 6 x (9 w x^{4} - 4 w - 3 x^{2})$

Step 1.4.4

Multiply $- 5$ by $- 11$ .

$- 40 w^{4} x + 55 w^{3} x^{2} + 6 x (9 w x^{4} - 4 w - 3 x^{2})$

Step 1.5

Apply the distributive property.

$- 40 w^{4} x + 55 w^{3} x^{2} + 6 x (9 w x^{4}) + 6 x (- 4 w) + 6 x (- 3 x^{2})$

Step 1.6

Simplify.

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Step 1.6.1

Multiply $x$ by $x^{4}$ by adding the exponents.

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Step 1.6.1.1

Move $x^{4}$ .

$- 40 w^{4} x + 55 w^{3} x^{2} + 6 (x^{4} x) (9 w) + 6 x (- 4 w) + 6 x (- 3 x^{2})$

Step 1.6.1.2

Multiply $x^{4}$ by $x$ .

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Step 1.6.1.2.1

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

$- 40 w^{4} x + 55 w^{3} x^{2} + 6 (x^{4} x^{1}) (9 w) + 6 x (- 4 w) + 6 x (- 3 x^{2})$

Step 1.6.1.2.2

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

$- 40 w^{4} x + 55 w^{3} x^{2} + 6 x^{4 + 1} (9 w) + 6 x (- 4 w) + 6 x (- 3 x^{2})$

Step 1.6.1.3

Add $4$ and $1$ .

$- 40 w^{4} x + 55 w^{3} x^{2} + 6 x^{5} (9 w) + 6 x (- 4 w) + 6 x (- 3 x^{2})$

Step 1.6.2

Rewrite using the commutative property of multiplication.

$- 40 w^{4} x + 55 w^{3} x^{2} + 6 x^{5} (9 w) + 6 \cdot - 4 x w + 6 x (- 3 x^{2})$

Step 1.6.3

Rewrite using the commutative property of multiplication.

$- 40 w^{4} x + 55 w^{3} x^{2} + 6 x^{5} (9 w) + 6 \cdot - 4 x w + 6 \cdot - 3 x \cdot x^{2}$

Step 1.7

Simplify each term.

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Step 1.7.1

Rewrite using the commutative property of multiplication.

$- 40 w^{4} x + 55 w^{3} x^{2} + 6 \cdot 9 x^{5} w + 6 \cdot - 4 x w + 6 \cdot - 3 x \cdot x^{2}$

Step 1.7.2

Multiply $6$ by $9$ .

$- 40 w^{4} x + 55 w^{3} x^{2} + 54 x^{5} w + 6 \cdot - 4 x w + 6 \cdot - 3 x \cdot x^{2}$

Step 1.7.3

Multiply $6$ by $- 4$ .

$- 40 w^{4} x + 55 w^{3} x^{2} + 54 x^{5} w - 24 x w + 6 \cdot - 3 x \cdot x^{2}$

Step 1.7.4

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

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Step 1.7.4.1

Move $x^{2}$ .

$- 40 w^{4} x + 55 w^{3} x^{2} + 54 x^{5} w - 24 x w + 6 \cdot - 3 (x^{2} x)$

Step 1.7.4.2

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

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Step 1.7.4.2.1

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

$- 40 w^{4} x + 55 w^{3} x^{2} + 54 x^{5} w - 24 x w + 6 \cdot - 3 (x^{2} x^{1})$

Step 1.7.4.2.2

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

$- 40 w^{4} x + 55 w^{3} x^{2} + 54 x^{5} w - 24 x w + 6 \cdot - 3 x^{2 + 1}$

Step 1.7.4.3

Add $2$ and $1$ .

$- 40 w^{4} x + 55 w^{3} x^{2} + 54 x^{5} w - 24 x w + 6 \cdot - 3 x^{3}$

Step 1.7.5

Multiply $6$ by $- 3$ .

$- 40 w^{4} x + 55 w^{3} x^{2} + 54 x^{5} w - 24 x w - 18 x^{3}$

Step 2

Simplify the expression.

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Step 2.1

Move $x^{5}$ .

$- 40 w^{4} x + 55 w^{3} x^{2} + 54 w x^{5} - 24 x w - 18 x^{3}$

Step 2.2

Move $x$ .

$- 40 w^{4} x + 55 w^{3} x^{2} + 54 w x^{5} - 24 w x - 18 x^{3}$

Step 2.3

Move $- 24 w x$ .

$- 40 w^{4} x + 55 w^{3} x^{2} + 54 w x^{5} - 18 x^{3} - 24 w x$

Step 2.4

Move $55 w^{3} x^{2}$ .

$- 40 w^{4} x + 54 w x^{5} + 55 w^{3} x^{2} - 18 x^{3} - 24 w x$

Step 2.5

Reorder $- 40 w^{4} x$ and $54 w x^{5}$ .

$54 w x^{5} - 40 w^{4} x + 55 w^{3} x^{2} - 18 x^{3} - 24 w x$