How do you expand #(5m^3-1)^3#?

1 Answer
Sep 24, 2016

# 25m^6 - 10m^3 + 1 #

Explanation:

# (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.

# (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.

# (5m^3 - 1)(5m^3 - 1) #
# 5m^3(5m^3) + 5m^3(-1) - 1(5m^3) - 1(-1) #
# 25m^6 - 5m^3 - 5m^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. # 5m^3 * 5m^3 = 5 * 5 * m^(3 +3) = 25m^6 #