Algebra Examples

$(- 8 x^{2} + 5 x^{4} - 7 + 4 x^{3}) - (- 4 - 2 x^{3} + 9 x^{4} - 3 x^{2})$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$- 8 x^{2} + 5 x^{4} - 7 + 4 x^{3} - - 4 - (- 2 x^{3}) - (9 x^{4}) - (- 3 x^{2})$

Step 1.2

Simplify.

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Step 1.2.1

Multiply $- 1$ by $- 4$ .

$- 8 x^{2} + 5 x^{4} - 7 + 4 x^{3} + 4 - (- 2 x^{3}) - (9 x^{4}) - (- 3 x^{2})$

Step 1.2.2

Multiply $- 2$ by $- 1$ .

$- 8 x^{2} + 5 x^{4} - 7 + 4 x^{3} + 4 + 2 x^{3} - (9 x^{4}) - (- 3 x^{2})$

Step 1.2.3

Multiply $9$ by $- 1$ .

$- 8 x^{2} + 5 x^{4} - 7 + 4 x^{3} + 4 + 2 x^{3} - 9 x^{4} - (- 3 x^{2})$

Step 1.2.4

Multiply $- 3$ by $- 1$ .

$- 8 x^{2} + 5 x^{4} - 7 + 4 x^{3} + 4 + 2 x^{3} - 9 x^{4} + 3 x^{2}$

Step 2

Simplify by adding terms.

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Step 2.1

Add $- 8 x^{2}$ and $3 x^{2}$ .

$5 x^{4} - 7 + 4 x^{3} + 4 + 2 x^{3} - 9 x^{4} - 5 x^{2}$

Step 2.2

Subtract $9 x^{4}$ from $5 x^{4}$ .

$- 4 x^{4} - 7 + 4 x^{3} + 4 + 2 x^{3} - 5 x^{2}$

Step 2.3

Add $- 7$ and $4$ .

$- 4 x^{4} + 4 x^{3} - 3 + 2 x^{3} - 5 x^{2}$

Step 2.4

Add $4 x^{3}$ and $2 x^{3}$ .

$- 4 x^{4} + 6 x^{3} - 3 - 5 x^{2}$

Step 2.5

Move $- 3$ .

$- 4 x^{4} + 6 x^{3} - 5 x^{2} - 3$