Algebra Examples

$(8 x^{5} + 6 x^{3} - 2 x^{2} + 10 x) - (9 x^{5} - x^{3} - 13 x^{2} + 4)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$8 x^{5} + 6 x^{3} - 2 x^{2} + 10 x - (9 x^{5}) - - x^{3} - (- 13 x^{2}) - 1 \cdot 4$

Step 1.2

Simplify.

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Step 1.2.1

Multiply $9$ by $- 1$ .

$8 x^{5} + 6 x^{3} - 2 x^{2} + 10 x - 9 x^{5} - - x^{3} - (- 13 x^{2}) - 1 \cdot 4$

Step 1.2.2

Multiply $- - x^{3}$ .

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Step 1.2.2.1

Multiply $- 1$ by $- 1$ .

$8 x^{5} + 6 x^{3} - 2 x^{2} + 10 x - 9 x^{5} + 1 x^{3} - (- 13 x^{2}) - 1 \cdot 4$

Step 1.2.2.2

Multiply $x^{3}$ by $1$ .

$8 x^{5} + 6 x^{3} - 2 x^{2} + 10 x - 9 x^{5} + x^{3} - (- 13 x^{2}) - 1 \cdot 4$

Step 1.2.3

Multiply $- 13$ by $- 1$ .

$8 x^{5} + 6 x^{3} - 2 x^{2} + 10 x - 9 x^{5} + x^{3} + 13 x^{2} - 1 \cdot 4$

Step 1.2.4

Multiply $- 1$ by $4$ .

$8 x^{5} + 6 x^{3} - 2 x^{2} + 10 x - 9 x^{5} + x^{3} + 13 x^{2} - 4$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $9 x^{5}$ from $8 x^{5}$ .

$- x^{5} + 6 x^{3} - 2 x^{2} + 10 x + x^{3} + 13 x^{2} - 4$

Step 2.2

Add $6 x^{3}$ and $x^{3}$ .

$- x^{5} + 7 x^{3} - 2 x^{2} + 10 x + 13 x^{2} - 4$

Step 2.3

Add $- 2 x^{2}$ and $13 x^{2}$ .

$- x^{5} + 7 x^{3} + 11 x^{2} + 10 x - 4$