Basic Math Examples

$A \cdot A a A \sqrt{5 (5 - a)} (5 - b) (5 - c) A$

Step 1

Multiply $A$ by $A$ .

$A^{2} a A \sqrt{5 (5 - a)} (5 - b) (5 - c) A$

Step 2

Multiply $A^{2}$ by $A$ by adding the exponents.

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Step 2.1

Move $A$ .

$A \cdot A^{2} a \sqrt{5 (5 - a)} (5 - b) (5 - c) A$

Step 2.2

Multiply $A$ by $A^{2}$ .

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Step 2.2.1

Raise $A$ to the power of $1$ .

$A^{1} A^{2} a \sqrt{5 (5 - a)} (5 - b) (5 - c) A$

Step 2.2.2

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

$A^{1 + 2} a \sqrt{5 (5 - a)} (5 - b) (5 - c) A$

Step 2.3

Add $1$ and $2$ .

$A^{3} a \sqrt{5 (5 - a)} (5 - b) (5 - c) A$

Step 3

Multiply $A^{3}$ by $A$ by adding the exponents.

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Step 3.1

Move $A$ .

$A \cdot A^{3} a \sqrt{5 (5 - a)} (5 - b) (5 - c)$

Step 3.2

Multiply $A$ by $A^{3}$ .

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Step 3.2.1

Raise $A$ to the power of $1$ .

$A^{1} A^{3} a \sqrt{5 (5 - a)} (5 - b) (5 - c)$

Step 3.2.2

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

$A^{1 + 3} a \sqrt{5 (5 - a)} (5 - b) (5 - c)$

Step 3.3

Add $1$ and $3$ .

$A^{4} a \sqrt{5 (5 - a)} (5 - b) (5 - c)$

Step 4

Simplify terms.

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Step 4.1

Apply the distributive property.

$(A^{4} a \sqrt{5 (5 - a)} \cdot 5 + A^{4} a \sqrt{5 (5 - a)} (- b)) (5 - c)$

Step 4.2

Reorder.

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Step 4.2.1

Move $5$ to the left of $A^{4} a \sqrt{5 (5 - a)}$ .

$(5 \cdot (A^{4} a \sqrt{5 (5 - a)}) + A^{4} a \sqrt{5 (5 - a)} (- b)) (5 - c)$

Step 4.2.2

Rewrite using the commutative property of multiplication.

$(5 \cdot (A^{4} a \sqrt{5 (5 - a)}) - A^{4} a \sqrt{5 (5 - a)} b) (5 - c)$

Step 4.3

Remove parentheses.

$(5 A^{4} a \sqrt{5 (5 - a)} - A^{4} a \sqrt{5 (5 - a)} b) (5 - c)$

Step 5

Expand $(5 A^{4} a \sqrt{5 (5 - a)} - A^{4} a \sqrt{5 (5 - a)} b) (5 - c)$ using the FOIL Method.

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Step 5.1

Apply the distributive property.

$5 A^{4} a \sqrt{5 (5 - a)} (5 - c) - A^{4} a \sqrt{5 (5 - a)} b (5 - c)$

Step 5.2

Apply the distributive property.

$5 A^{4} a \sqrt{5 (5 - a)} \cdot 5 + 5 A^{4} a \sqrt{5 (5 - a)} (- c) - A^{4} a \sqrt{5 (5 - a)} b (5 - c)$

Step 5.3

Apply the distributive property.

$5 A^{4} a \sqrt{5 (5 - a)} \cdot 5 + 5 A^{4} a \sqrt{5 (5 - a)} (- c) - A^{4} a \sqrt{5 (5 - a)} b \cdot 5 - A^{4} a \sqrt{5 (5 - a)} b (- c)$

Step 6

Simplify each term.

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Step 6.1

Multiply $5$ by $5$ .

$25 A^{4} a \sqrt{5 (5 - a)} + 5 A^{4} a \sqrt{5 (5 - a)} (- c) - A^{4} a \sqrt{5 (5 - a)} b \cdot 5 - A^{4} a \sqrt{5 (5 - a)} b (- c)$

Step 6.2

Multiply $- 1$ by $5$ .

$25 A^{4} a \sqrt{5 (5 - a)} - 5 A^{4} a \sqrt{5 (5 - a)} c - A^{4} a \sqrt{5 (5 - a)} b \cdot 5 - A^{4} a \sqrt{5 (5 - a)} b (- c)$

Step 6.3

Multiply $5$ by $- 1$ .

$25 A^{4} a \sqrt{5 (5 - a)} - 5 A^{4} a \sqrt{5 (5 - a)} c - 5 A^{4} a \sqrt{5 (5 - a)} b - A^{4} a \sqrt{5 (5 - a)} b (- c)$

Step 6.4

Multiply $- A^{4} a \sqrt{5 (5 - a)} b (- c)$ .

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Step 6.4.1

Multiply $- 1$ by $- 1$ .

$25 A^{4} a \sqrt{5 (5 - a)} - 5 A^{4} a \sqrt{5 (5 - a)} c - 5 A^{4} a \sqrt{5 (5 - a)} b + 1 A^{4} a \sqrt{5 (5 - a)} b c$

Step 6.4.2

Multiply $A^{4}$ by $1$ .

$25 A^{4} a \sqrt{5 (5 - a)} - 5 A^{4} a \sqrt{5 (5 - a)} c - 5 A^{4} a \sqrt{5 (5 - a)} b + A^{4} a \sqrt{5 (5 - a)} b c$