Algebra Examples

$(10 x^{4} - 4 x^{3} - 7 x^{2} + 5 x + 9) - (2 x^{4} - 5 x^{3} - 4 x^{2} + 9 x + 3)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$10 x^{4} - 4 x^{3} - 7 x^{2} + 5 x + 9 - (2 x^{4}) - (- 5 x^{3}) - (- 4 x^{2}) - (9 x) - 1 \cdot 3$

Step 1.2

Simplify.

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Step 1.2.1

Multiply $2$ by $- 1$ .

$10 x^{4} - 4 x^{3} - 7 x^{2} + 5 x + 9 - 2 x^{4} - (- 5 x^{3}) - (- 4 x^{2}) - (9 x) - 1 \cdot 3$

Step 1.2.2

Multiply $- 5$ by $- 1$ .

$10 x^{4} - 4 x^{3} - 7 x^{2} + 5 x + 9 - 2 x^{4} + 5 x^{3} - (- 4 x^{2}) - (9 x) - 1 \cdot 3$

Step 1.2.3

Multiply $- 4$ by $- 1$ .

$10 x^{4} - 4 x^{3} - 7 x^{2} + 5 x + 9 - 2 x^{4} + 5 x^{3} + 4 x^{2} - (9 x) - 1 \cdot 3$

Step 1.2.4

Multiply $9$ by $- 1$ .

$10 x^{4} - 4 x^{3} - 7 x^{2} + 5 x + 9 - 2 x^{4} + 5 x^{3} + 4 x^{2} - 9 x - 1 \cdot 3$

Step 1.2.5

Multiply $- 1$ by $3$ .

$10 x^{4} - 4 x^{3} - 7 x^{2} + 5 x + 9 - 2 x^{4} + 5 x^{3} + 4 x^{2} - 9 x - 3$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $2 x^{4}$ from $10 x^{4}$ .

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

Step 2.2

Add $- 4 x^{3}$ and $5 x^{3}$ .

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

Step 2.3

Add $- 7 x^{2}$ and $4 x^{2}$ .

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

Step 2.4

Subtract $9 x$ from $5 x$ .

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

Step 2.5

Subtract $3$ from $9$ .

$8 x^{4} + x^{3} - 3 x^{2} - 4 x + 6$