Algebra Examples

$(2 p^{4} - 4 p^{3} - 4 p) - (8 p^{4} - 2 p^{3} - 2 p^{2} - 3 p)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$2 p^{4} - 4 p^{3} - 4 p - (8 p^{4}) - (- 2 p^{3}) - (- 2 p^{2}) - (- 3 p)$

Step 1.2

Simplify.

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Step 1.2.1

Multiply $8$ by $- 1$ .

$2 p^{4} - 4 p^{3} - 4 p - 8 p^{4} - (- 2 p^{3}) - (- 2 p^{2}) - (- 3 p)$

Step 1.2.2

Multiply $- 2$ by $- 1$ .

$2 p^{4} - 4 p^{3} - 4 p - 8 p^{4} + 2 p^{3} - (- 2 p^{2}) - (- 3 p)$

Step 1.2.3

Multiply $- 2$ by $- 1$ .

$2 p^{4} - 4 p^{3} - 4 p - 8 p^{4} + 2 p^{3} + 2 p^{2} - (- 3 p)$

Step 1.2.4

Multiply $- 3$ by $- 1$ .

$2 p^{4} - 4 p^{3} - 4 p - 8 p^{4} + 2 p^{3} + 2 p^{2} + 3 p$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $8 p^{4}$ from $2 p^{4}$ .

$- 6 p^{4} - 4 p^{3} - 4 p + 2 p^{3} + 2 p^{2} + 3 p$

Step 2.2

Add $- 4 p^{3}$ and $2 p^{3}$ .

$- 6 p^{4} - 2 p^{3} - 4 p + 2 p^{2} + 3 p$

Step 2.3

Add $- 4 p$ and $3 p$ .

$- 6 p^{4} - 2 p^{3} + 2 p^{2} - p$