Basic Math Examples

$(3 a^{2} - 2 a - a^{3}) - (5^{2} - a^{3} - 8 a)$

Step 1

Simplify each term.

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Step 1.1

Raise $5$ to the power of $2$ .

$3 a^{2} - 2 a - a^{3} - (25 - a^{3} - 8 a)$

Step 1.2

Apply the distributive property.

$3 a^{2} - 2 a - a^{3} - 1 \cdot 25 - - a^{3} - (- 8 a)$

Step 1.3

Simplify.

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Step 1.3.1

Multiply $- 1$ by $25$ .

$3 a^{2} - 2 a - a^{3} - 25 - - a^{3} - (- 8 a)$

Step 1.3.2

Multiply $- - a^{3}$ .

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Step 1.3.2.1

Multiply $- 1$ by $- 1$ .

$3 a^{2} - 2 a - a^{3} - 25 + 1 a^{3} - (- 8 a)$

Step 1.3.2.2

Multiply $a^{3}$ by $1$ .

$3 a^{2} - 2 a - a^{3} - 25 + a^{3} - (- 8 a)$

Step 1.3.3

Multiply $- 8$ by $- 1$ .

$3 a^{2} - 2 a - a^{3} - 25 + a^{3} + 8 a$

Step 2

Simplify by adding terms.

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Step 2.1

Combine the opposite terms in $3 a^{2} - 2 a - a^{3} - 25 + a^{3} + 8 a$ .

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Step 2.1.1

Add $- a^{3}$ and $a^{3}$ .

$3 a^{2} - 2 a + 0 - 25 + 8 a$

Step 2.1.2

Add $3 a^{2} - 2 a$ and $0$ .

$3 a^{2} - 2 a - 25 + 8 a$

Step 2.2

Add $- 2 a$ and $8 a$ .

$3 a^{2} + 6 a - 25$