Algebra Examples

$a^{2} (m - 7 a^{3}) - m (a^{2} - 10)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$a^{2} m + a^{2} (- 7 a^{3}) - m (a^{2} - 10)$

Step 1.2

Rewrite using the commutative property of multiplication.

$a^{2} m - 7 a^{2} a^{3} - m (a^{2} - 10)$

Step 1.3

Multiply $a^{2}$ by $a^{3}$ by adding the exponents.

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Step 1.3.1

Move $a^{3}$ .

$a^{2} m - 7 (a^{3} a^{2}) - m (a^{2} - 10)$

Step 1.3.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$a^{2} m - 7 a^{3 + 2} - m (a^{2} - 10)$

Step 1.3.3

Add $3$ and $2$ .

$a^{2} m - 7 a^{5} - m (a^{2} - 10)$

Step 1.4

Apply the distributive property.

$a^{2} m - 7 a^{5} - m a^{2} - m \cdot - 10$

Step 1.5

Multiply $- 10$ by $- 1$ .

$a^{2} m - 7 a^{5} - m a^{2} + 10 m$

Step 2

Combine the opposite terms in $a^{2} m - 7 a^{5} - m a^{2} + 10 m$ .

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Step 2.1

Reorder the factors in the terms $a^{2} m$ and $- m a^{2}$ .

$a^{2} m - 7 a^{5} - a^{2} m + 10 m$

Step 2.2

Subtract $a^{2} m$ from $a^{2} m$ .

$- 7 a^{5} + 0 + 10 m$

Step 2.3

Add $- 7 a^{5}$ and $0$ .

$- 7 a^{5} + 10 m$