Basic Math Examples

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

Step 1

Use the Binomial Theorem.

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

Step 2

Simplify each term.

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Step 2.1

Multiply the exponents in ${(a^{2})}^{3}$ .

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Step 2.1.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Step 2.1.2

Multiply $2$ by $3$ .

$a^{6} + 3 {(a^{2})}^{2} \cdot - 5 + 3 a^{2} {(- 5)}^{2} + {(- 5)}^{3}$

Step 2.2

Multiply the exponents in ${(a^{2})}^{2}$ .

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Step 2.2.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$a^{6} + 3 a^{2 \cdot 2} \cdot - 5 + 3 a^{2} {(- 5)}^{2} + {(- 5)}^{3}$

Step 2.2.2

Multiply $2$ by $2$ .

$a^{6} + 3 a^{4} \cdot - 5 + 3 a^{2} {(- 5)}^{2} + {(- 5)}^{3}$

Step 2.3

Multiply $- 5$ by $3$ .

$a^{6} - 15 a^{4} + 3 a^{2} {(- 5)}^{2} + {(- 5)}^{3}$

Step 2.4

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

$a^{6} - 15 a^{4} + 3 a^{2} \cdot 25 + {(- 5)}^{3}$

Step 2.5

Multiply $25$ by $3$ .

$a^{6} - 15 a^{4} + 75 a^{2} + {(- 5)}^{3}$

Step 2.6

Raise $- 5$ to the power of $3$ .

$a^{6} - 15 a^{4} + 75 a^{2} - 125$