Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$- 4 x^{7} + 2 x^{9} + 9 + 9 x^{8} - 1 \cdot 5 - (- 3 x^{8}) - (8 x^{9}) - (7 x^{7})$

Step 1.2

Simplify.

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Step 1.2.1

Multiply $- 1$ by $5$ .

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

Step 1.2.2

Multiply $- 3$ by $- 1$ .

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

Step 1.2.3

Multiply $8$ by $- 1$ .

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

Step 1.2.4

Multiply $7$ by $- 1$ .

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

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $7 x^{7}$ from $- 4 x^{7}$ .

$2 x^{9} + 9 + 9 x^{8} - 5 + 3 x^{8} - 8 x^{9} - 11 x^{7}$

Step 2.2

Subtract $8 x^{9}$ from $2 x^{9}$ .

$- 6 x^{9} + 9 + 9 x^{8} - 5 + 3 x^{8} - 11 x^{7}$

Step 2.3

Subtract $5$ from $9$ .

$- 6 x^{9} + 9 x^{8} + 4 + 3 x^{8} - 11 x^{7}$

Step 2.4

Add $9 x^{8}$ and $3 x^{8}$ .

$- 6 x^{9} + 12 x^{8} + 4 - 11 x^{7}$