Algebra Examples

$(7 x^{4} - 3 x^{3} + 5 x^{2} + 8 x - 11) - (3 x^{4} - 9 x^{3} - 4 x^{2} + 12 x + 4)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$7 x^{4} - 3 x^{3} + 5 x^{2} + 8 x - 11 - (3 x^{4}) - (- 9 x^{3}) - (- 4 x^{2}) - (12 x) - 1 \cdot 4$

Step 1.2

Simplify.

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Step 1.2.1

Multiply $3$ by $- 1$ .

$7 x^{4} - 3 x^{3} + 5 x^{2} + 8 x - 11 - 3 x^{4} - (- 9 x^{3}) - (- 4 x^{2}) - (12 x) - 1 \cdot 4$

Step 1.2.2

Multiply $- 9$ by $- 1$ .

$7 x^{4} - 3 x^{3} + 5 x^{2} + 8 x - 11 - 3 x^{4} + 9 x^{3} - (- 4 x^{2}) - (12 x) - 1 \cdot 4$

Step 1.2.3

Multiply $- 4$ by $- 1$ .

$7 x^{4} - 3 x^{3} + 5 x^{2} + 8 x - 11 - 3 x^{4} + 9 x^{3} + 4 x^{2} - (12 x) - 1 \cdot 4$

Step 1.2.4

Multiply $12$ by $- 1$ .

$7 x^{4} - 3 x^{3} + 5 x^{2} + 8 x - 11 - 3 x^{4} + 9 x^{3} + 4 x^{2} - 12 x - 1 \cdot 4$

Step 1.2.5

Multiply $- 1$ by $4$ .

$7 x^{4} - 3 x^{3} + 5 x^{2} + 8 x - 11 - 3 x^{4} + 9 x^{3} + 4 x^{2} - 12 x - 4$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $3 x^{4}$ from $7 x^{4}$ .

$4 x^{4} - 3 x^{3} + 5 x^{2} + 8 x - 11 + 9 x^{3} + 4 x^{2} - 12 x - 4$

Step 2.2

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

$4 x^{4} + 6 x^{3} + 5 x^{2} + 8 x - 11 + 4 x^{2} - 12 x - 4$

Step 2.3

Add $5 x^{2}$ and $4 x^{2}$ .

$4 x^{4} + 6 x^{3} + 9 x^{2} + 8 x - 11 - 12 x - 4$

Step 2.4

Subtract $12 x$ from $8 x$ .

$4 x^{4} + 6 x^{3} + 9 x^{2} - 4 x - 11 - 4$

Step 2.5

Subtract $4$ from $- 11$ .

$4 x^{4} + 6 x^{3} + 9 x^{2} - 4 x - 15$