Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Simplify.

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Step 1.2.1

Multiply $7$ by $- 1$ .

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

Step 1.2.2

Multiply $- 3$ by $- 1$ .

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

Step 1.2.3

Multiply $- 1$ by $1$ .

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

Step 2

Simplify by adding terms.

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Step 2.1

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

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

Step 2.2

Subtract $7 x^{2}$ from $5 x^{2}$ .

$- 4 x^{3} - 2 x^{2} + 10 x + 4 + 3 x - 1$

Step 2.3

Add $10 x$ and $3 x$ .

$- 4 x^{3} - 2 x^{2} + 13 x + 4 - 1$

Step 2.4

Subtract $1$ from $4$ .

$- 4 x^{3} - 2 x^{2} + 13 x + 3$