Algebra Examples

$(7 x^{4} - 5 x^{3} + 8 x^{2} + 9 x - 13) - (2 x^{4} + 6 x^{3} - 4 x^{2} - x + 4)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$7 x^{4} - 5 x^{3} + 8 x^{2} + 9 x - 13 - (2 x^{4}) - (6 x^{3}) - (- 4 x^{2}) - - x - 1 \cdot 4$

Step 1.2

Simplify.

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Step 1.2.1

Multiply $2$ by $- 1$ .

$7 x^{4} - 5 x^{3} + 8 x^{2} + 9 x - 13 - 2 x^{4} - (6 x^{3}) - (- 4 x^{2}) - - x - 1 \cdot 4$

Step 1.2.2

Multiply $6$ by $- 1$ .

$7 x^{4} - 5 x^{3} + 8 x^{2} + 9 x - 13 - 2 x^{4} - 6 x^{3} - (- 4 x^{2}) - - x - 1 \cdot 4$

Step 1.2.3

Multiply $- 4$ by $- 1$ .

$7 x^{4} - 5 x^{3} + 8 x^{2} + 9 x - 13 - 2 x^{4} - 6 x^{3} + 4 x^{2} - - x - 1 \cdot 4$

Step 1.2.4

Multiply $- - x$ .

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Step 1.2.4.1

Multiply $- 1$ by $- 1$ .

$7 x^{4} - 5 x^{3} + 8 x^{2} + 9 x - 13 - 2 x^{4} - 6 x^{3} + 4 x^{2} + 1 x - 1 \cdot 4$

Step 1.2.4.2

Multiply $x$ by $1$ .

$7 x^{4} - 5 x^{3} + 8 x^{2} + 9 x - 13 - 2 x^{4} - 6 x^{3} + 4 x^{2} + x - 1 \cdot 4$

Step 1.2.5

Multiply $- 1$ by $4$ .

$7 x^{4} - 5 x^{3} + 8 x^{2} + 9 x - 13 - 2 x^{4} - 6 x^{3} + 4 x^{2} + x - 4$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $2 x^{4}$ from $7 x^{4}$ .

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

Step 2.2

Subtract $6 x^{3}$ from $- 5 x^{3}$ .

$5 x^{4} - 11 x^{3} + 8 x^{2} + 9 x - 13 + 4 x^{2} + x - 4$

Step 2.3

Add $8 x^{2}$ and $4 x^{2}$ .

$5 x^{4} - 11 x^{3} + 12 x^{2} + 9 x - 13 + x - 4$

Step 2.4

Add $9 x$ and $x$ .

$5 x^{4} - 11 x^{3} + 12 x^{2} + 10 x - 13 - 4$

Step 2.5

Subtract $4$ from $- 13$ .

$5 x^{4} - 11 x^{3} + 12 x^{2} + 10 x - 17$