Algebra Examples

$(6 - r^{2} + 5 r^{3}) + (8 r^{2} - r^{3} + 4) - (3 r^{3} - r^{2} - 4)$

Step 1

Remove parentheses.

$6 - r^{2} + 5 r^{3} + 8 r^{2} - r^{3} + 4 - (3 r^{3} - r^{2} - 4)$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$6 - r^{2} + 5 r^{3} + 8 r^{2} - r^{3} + 4 - (3 r^{3}) - - r^{2} - - 4$

Step 2.2

Simplify.

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Step 2.2.1

Multiply $3$ by $- 1$ .

$6 - r^{2} + 5 r^{3} + 8 r^{2} - r^{3} + 4 - 3 r^{3} - - r^{2} - - 4$

Step 2.2.2

Multiply $- - r^{2}$ .

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Step 2.2.2.1

Multiply $- 1$ by $- 1$ .

$6 - r^{2} + 5 r^{3} + 8 r^{2} - r^{3} + 4 - 3 r^{3} + 1 r^{2} - - 4$

Step 2.2.2.2

Multiply $r^{2}$ by $1$ .

$6 - r^{2} + 5 r^{3} + 8 r^{2} - r^{3} + 4 - 3 r^{3} + r^{2} - - 4$

Step 2.2.3

Multiply $- 1$ by $- 4$ .

$6 - r^{2} + 5 r^{3} + 8 r^{2} - r^{3} + 4 - 3 r^{3} + r^{2} + 4$

Step 3

Simplify by adding terms.

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Step 3.1

Combine the opposite terms in $6 - r^{2} + 5 r^{3} + 8 r^{2} - r^{3} + 4 - 3 r^{3} + r^{2} + 4$ .

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Step 3.1.1

Add $- r^{2}$ and $r^{2}$ .

$6 + 5 r^{3} + 8 r^{2} - r^{3} + 4 - 3 r^{3} + 0 + 4$

Step 3.1.2

Add $6 + 5 r^{3} + 8 r^{2} - r^{3} + 4 - 3 r^{3}$ and $0$ .

$6 + 5 r^{3} + 8 r^{2} - r^{3} + 4 - 3 r^{3} + 4$

Step 3.2

Add $6$ and $4$ .

$5 r^{3} + 8 r^{2} - r^{3} + 10 - 3 r^{3} + 4$

Step 3.3

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

$4 r^{3} + 8 r^{2} + 10 - 3 r^{3} + 4$

Step 3.4

Subtract $3 r^{3}$ from $4 r^{3}$ .

$r^{3} + 8 r^{2} + 10 + 4$

Step 3.5

Add $10$ and $4$ .

$r^{3} + 8 r^{2} + 14$