Basic Math Examples

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

Step 1

Apply the distributive property.

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

Step 2

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

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Step 2.1

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

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

Step 2.2

Add $m$ and $m$ .

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

Step 2.3

Subtract $2$ from $- 3$ .

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

Step 3

Rewrite using the commutative property of multiplication.

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

Step 4

Simplify each term.

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Step 4.1

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

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Step 4.1.1

Move $a^{3 - m}$ .

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

Step 4.1.2

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

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

Step 4.1.3

Combine the opposite terms in $3 - m + m - 3$ .

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Step 4.1.3.1

Add $- m$ and $m$ .

$a^{2 m - 5} - a^{3 + 0 - 3}$

Step 4.1.3.2

Add $3$ and $0$ .

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

Step 4.1.3.3

Subtract $3$ from $3$ .

$a^{2 m - 5} - a^{0}$

Step 4.2

Simplify $- a^{0}$ .

$a^{2 m - 5} - 1$