Algebra Examples

$(5 x^{4} + 3 x^{6} - 5 + 7 x^{5}) - (7 - 3 x^{5} + 8 x^{6} + 9 x^{4})$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$5 x^{4} + 3 x^{6} - 5 + 7 x^{5} - 1 \cdot 7 - (- 3 x^{5}) - (8 x^{6}) - (9 x^{4})$

Step 1.2

Simplify.

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Step 1.2.1

Multiply $- 1$ by $7$ .

$5 x^{4} + 3 x^{6} - 5 + 7 x^{5} - 7 - (- 3 x^{5}) - (8 x^{6}) - (9 x^{4})$

Step 1.2.2

Multiply $- 3$ by $- 1$ .

$5 x^{4} + 3 x^{6} - 5 + 7 x^{5} - 7 + 3 x^{5} - (8 x^{6}) - (9 x^{4})$

Step 1.2.3

Multiply $8$ by $- 1$ .

$5 x^{4} + 3 x^{6} - 5 + 7 x^{5} - 7 + 3 x^{5} - 8 x^{6} - (9 x^{4})$

Step 1.2.4

Multiply $9$ by $- 1$ .

$5 x^{4} + 3 x^{6} - 5 + 7 x^{5} - 7 + 3 x^{5} - 8 x^{6} - 9 x^{4}$

Step 2

Simplify by adding terms.

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Step 2.1

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

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

Step 2.2

Subtract $8 x^{6}$ from $3 x^{6}$ .

$- 5 x^{6} - 5 + 7 x^{5} - 7 + 3 x^{5} - 4 x^{4}$

Step 2.3

Subtract $7$ from $- 5$ .

$- 5 x^{6} + 7 x^{5} - 12 + 3 x^{5} - 4 x^{4}$

Step 2.4

Add $7 x^{5}$ and $3 x^{5}$ .

$- 5 x^{6} + 10 x^{5} - 12 - 4 x^{4}$

Step 2.5

Move $- 12$ .

$- 5 x^{6} + 10 x^{5} - 4 x^{4} - 12$