How do you expand ${(5 m^{3} - 1)}^{3}$ $(5m^3-1)^3$ ?

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How do you expand ${(5 m^{3} - 1)}^{3}$ $(5m^3-1)^3$ ?

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Answer 1 · 2016-09-24T01:54:18

$25 m^{6} - 10 m^{3} + 1$ $25m^6 - 10m^3 + 1$

Explanation:

${(5 m^{3} - 1)}^{3}$ $(5m^3 - 1)^3$

First step: expand the brackets. To expand the above question, we have to remember that when we have a power/exponent/a little number above the brackets i.e. "n" , it means we have to multiply the function/number/letter in front, "n" number of times.

$(5 m^{3} - 1) (5 m^{3} - 1) (5 m^{3} - 1)$ $(5m^3 - 1)(5m^3 - 1)(5m^3 - 1)$

Second step: simplify the equation by multiplying the first two brackets and leaving the third bracket, constant.

$(5 m^{3} - 1) (5 m^{3} - 1)$ $(5m^3 - 1)(5m^3 - 1)$
$5 m^{3} (5 m^{3}) + 5 m^{3} (- 1) - 1 (5 m^{3}) - 1 (- 1)$ $5m^3(5m^3) + 5m^3(-1) - 1(5m^3) - 1(-1)$
$25 m^{6} - 5 m^{3} - 5 m^{3} + 1$ $25m^6 - 5m^3 - 5m^3 + 1$
$25 m^{6} - 10 m^{3} + 1$ $25m^6 - 10m^3 + 1$

Note: when multiplying numbers that have powers, you must add the powers but multiply the numbers.
E.g. $5 m^{3} \cdot 5 m^{3} = 5 \cdot 5 \cdot m^{3 + 3} = 25 m^{6}$ $5m^3 * 5m^3 = 5 * 5 * m^(3 +3) = 25m^6$

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How do you expand ${(5 m^{3} - 1)}^{3}$ $(5m^3-1)^3$ ?

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