Algebra Examples

$(- 7 d^{3} + 5 d + 5 d^{2} - 6 d^{4}) - (8 d + 5 d^{2} + 2 d^{4} + 3 d^{3})$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$- 7 d^{3} + 5 d + 5 d^{2} - 6 d^{4} - (8 d) - (5 d^{2}) - (2 d^{4}) - (3 d^{3})$

Step 1.2

Simplify.

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Step 1.2.1

Multiply $8$ by $- 1$ .

$- 7 d^{3} + 5 d + 5 d^{2} - 6 d^{4} - 8 d - (5 d^{2}) - (2 d^{4}) - (3 d^{3})$

Step 1.2.2

Multiply $5$ by $- 1$ .

$- 7 d^{3} + 5 d + 5 d^{2} - 6 d^{4} - 8 d - 5 d^{2} - (2 d^{4}) - (3 d^{3})$

Step 1.2.3

Multiply $2$ by $- 1$ .

$- 7 d^{3} + 5 d + 5 d^{2} - 6 d^{4} - 8 d - 5 d^{2} - 2 d^{4} - (3 d^{3})$

Step 1.2.4

Multiply $3$ by $- 1$ .

$- 7 d^{3} + 5 d + 5 d^{2} - 6 d^{4} - 8 d - 5 d^{2} - 2 d^{4} - 3 d^{3}$

Step 2

Simplify by adding terms.

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Step 2.1

Combine the opposite terms in $- 7 d^{3} + 5 d + 5 d^{2} - 6 d^{4} - 8 d - 5 d^{2} - 2 d^{4} - 3 d^{3}$ .

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Step 2.1.1

Subtract $5 d^{2}$ from $5 d^{2}$ .

$- 7 d^{3} + 5 d - 6 d^{4} - 8 d + 0 - 2 d^{4} - 3 d^{3}$

Step 2.1.2

Add $- 7 d^{3} + 5 d - 6 d^{4} - 8 d$ and $0$ .

$- 7 d^{3} + 5 d - 6 d^{4} - 8 d - 2 d^{4} - 3 d^{3}$

Step 2.2

Subtract $3 d^{3}$ from $- 7 d^{3}$ .

$- 10 d^{3} + 5 d - 6 d^{4} - 8 d - 2 d^{4}$

Step 2.3

Subtract $8 d$ from $5 d$ .

$- 10 d^{3} - 6 d^{4} - 3 d - 2 d^{4}$

Step 2.4

Subtract $2 d^{4}$ from $- 6 d^{4}$ .

$- 10 d^{3} - 8 d^{4} - 3 d$

Step 2.5

Reorder $- 10 d^{3}$ and $- 8 d^{4}$ .

$- 8 d^{4} - 10 d^{3} - 3 d$