Algebra Examples

$(6 r + 2 + 8 r^{3}) - (5 r^{3} - 11 - 8 r^{5}) - (6 r + 9 r^{5})$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$6 r + 2 + 8 r^{3} - (5 r^{3}) - - 11 - (- 8 r^{5}) - (6 r + 9 r^{5})$

Step 1.2

Simplify.

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Step 1.2.1

Multiply $5$ by $- 1$ .

$6 r + 2 + 8 r^{3} - 5 r^{3} - - 11 - (- 8 r^{5}) - (6 r + 9 r^{5})$

Step 1.2.2

Multiply $- 1$ by $- 11$ .

$6 r + 2 + 8 r^{3} - 5 r^{3} + 11 - (- 8 r^{5}) - (6 r + 9 r^{5})$

Step 1.2.3

Multiply $- 8$ by $- 1$ .

$6 r + 2 + 8 r^{3} - 5 r^{3} + 11 + 8 r^{5} - (6 r + 9 r^{5})$

Step 1.3

Apply the distributive property.

$6 r + 2 + 8 r^{3} - 5 r^{3} + 11 + 8 r^{5} - (6 r) - (9 r^{5})$

Step 1.4

Multiply $6$ by $- 1$ .

$6 r + 2 + 8 r^{3} - 5 r^{3} + 11 + 8 r^{5} - 6 r - (9 r^{5})$

Step 1.5

Multiply $9$ by $- 1$ .

$6 r + 2 + 8 r^{3} - 5 r^{3} + 11 + 8 r^{5} - 6 r - 9 r^{5}$

Step 2

Simplify by adding terms.

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Step 2.1

Combine the opposite terms in $6 r + 2 + 8 r^{3} - 5 r^{3} + 11 + 8 r^{5} - 6 r - 9 r^{5}$ .

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Step 2.1.1

Subtract $6 r$ from $6 r$ .

$2 + 8 r^{3} - 5 r^{3} + 11 + 8 r^{5} + 0 - 9 r^{5}$

Step 2.1.2

Add $2 + 8 r^{3} - 5 r^{3} + 11 + 8 r^{5}$ and $0$ .

$2 + 8 r^{3} - 5 r^{3} + 11 + 8 r^{5} - 9 r^{5}$

Step 2.2

Add $2$ and $11$ .

$8 r^{3} - 5 r^{3} + 13 + 8 r^{5} - 9 r^{5}$

Step 2.3

Subtract $5 r^{3}$ from $8 r^{3}$ .

$3 r^{3} + 13 + 8 r^{5} - 9 r^{5}$

Step 2.4

Subtract $9 r^{5}$ from $8 r^{5}$ .

$3 r^{3} + 13 - r^{5}$

Step 2.5

Simplify the expression.

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Step 2.5.1

Move $13$ .

$3 r^{3} - r^{5} + 13$

Step 2.5.2

Reorder $3 r^{3}$ and $- r^{5}$ .

$- r^{5} + 3 r^{3} + 13$