Write the binomial
1 − 27b3
as the difference of cubes.
what is (1^3-(3b)^3)?
I will be happy to check your answer. You need to memorize the two factors of
a^3-b^3
To write the binomial 1 - 27b^3 as the difference of cubes, we need to recognize the pattern of a^3 - b^3.
The pattern for the difference of cubes is a^3 - b^3 = (a - b)(a^2 + ab + b^2).
In this case, we have 1 - 27b^3, where a is 1 and b is (3b)^3. So we can rewrite it as:
1 - 27b^3 = (1 - (3b)^3)(1^2 + 1(3b) + (3b)^2)
The cube of (3b) is 27b^3, so we can substitute that back in:
1 - 27b^3 = (1 - 27b^3)(1 + 3b + 9b^2)