Algebra Examples

$(a^{3} - 2 a + 5) - (4 a^{3} - 5 a^{2} + a - 2)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$a^{3} - 2 a + 5 - (4 a^{3}) - (- 5 a^{2}) - a - - 2$

Step 1.2

Simplify.

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Step 1.2.1

Multiply $4$ by $- 1$ .

$a^{3} - 2 a + 5 - 4 a^{3} - (- 5 a^{2}) - a - - 2$

Step 1.2.2

Multiply $- 5$ by $- 1$ .

$a^{3} - 2 a + 5 - 4 a^{3} + 5 a^{2} - a - - 2$

Step 1.2.3

Multiply $- 1$ by $- 2$ .

$a^{3} - 2 a + 5 - 4 a^{3} + 5 a^{2} - a + 2$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $4 a^{3}$ from $a^{3}$ .

$- 3 a^{3} - 2 a + 5 + 5 a^{2} - a + 2$

Step 2.2

Subtract $a$ from $- 2 a$ .

$- 3 a^{3} - 3 a + 5 + 5 a^{2} + 2$

Step 2.3

Simplify the expression.

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Step 2.3.1

Add $5$ and $2$ .

$- 3 a^{3} - 3 a + 5 a^{2} + 7$

Step 2.3.2

Move $- 3 a$ .

$- 3 a^{3} + 5 a^{2} - 3 a + 7$