How do you find the product #(2a-b)^3#?

1 Answer
Jul 15, 2017

Answer:

The solution is: #8a^3-12a^2b+6ab^2-b^3#

Explanation:

There may be a more efficient and compact way, and someone may explain it, but I'd tend to just brute-force it. ;-)

#(2a-b)^3=(2a-b)(2a-b)(2a-b)#

Ignore the third bracket for now and do 'FOIL (first, outers, inners, lasts) on the first two brackets:

#(2a-b)(2a-b)(2a-b) = (4a^2-2ab-2ab+b^2)(2a-b)#

Collect like terms:

#(4a^2-4ab+b^2)(2a-b)#

Now multiply each term in the left bracket by each term in the right:

#8a^3-4a^2b-8a^2b+4ab^2+2ab^2-b^3#

Collect like terms again:

#8a^3-12a^2b+6ab^2-b^3#

And we're done!