Algebra Examples

$(7 r^{3} + 6 + 7 r^{2} - 4 r^{4}) - (- 7 r^{4} + 8 r^{2} - 8 r^{3} - 8)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$7 r^{3} + 6 + 7 r^{2} - 4 r^{4} - (- 7 r^{4}) - (8 r^{2}) - (- 8 r^{3}) - - 8$

Step 1.2

Simplify.

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Step 1.2.1

Multiply $- 7$ by $- 1$ .

$7 r^{3} + 6 + 7 r^{2} - 4 r^{4} + 7 r^{4} - (8 r^{2}) - (- 8 r^{3}) - - 8$

Step 1.2.2

Multiply $8$ by $- 1$ .

$7 r^{3} + 6 + 7 r^{2} - 4 r^{4} + 7 r^{4} - 8 r^{2} - (- 8 r^{3}) - - 8$

Step 1.2.3

Multiply $- 8$ by $- 1$ .

$7 r^{3} + 6 + 7 r^{2} - 4 r^{4} + 7 r^{4} - 8 r^{2} + 8 r^{3} - - 8$

Step 1.2.4

Multiply $- 1$ by $- 8$ .

$7 r^{3} + 6 + 7 r^{2} - 4 r^{4} + 7 r^{4} - 8 r^{2} + 8 r^{3} + 8$

Step 2

Simplify by adding terms.

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Step 2.1

Add $7 r^{3}$ and $8 r^{3}$ .

$15 r^{3} + 6 + 7 r^{2} - 4 r^{4} + 7 r^{4} - 8 r^{2} + 8$

Step 2.2

Add $6$ and $8$ .

$15 r^{3} + 7 r^{2} - 4 r^{4} + 7 r^{4} - 8 r^{2} + 14$

Step 2.3

Subtract $8 r^{2}$ from $7 r^{2}$ .

$15 r^{3} - 4 r^{4} + 7 r^{4} - r^{2} + 14$

Step 2.4

Add $- 4 r^{4}$ and $7 r^{4}$ .

$15 r^{3} + 3 r^{4} - r^{2} + 14$

Step 2.5

Reorder $15 r^{3}$ and $3 r^{4}$ .

$3 r^{4} + 15 r^{3} - r^{2} + 14$