%5E3-answer.jpeg "(2ab)^3 Answer")
Cube of a Binomial: (2ab)^3
In algebra, when we raise a binomial to a power, we need to follow certain rules to expand the expression correctly. In this article, we will explore the cube of the binomial (2ab)^3.
The Formula
The formula to cube a binomial is:
(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3
Applying the Formula
In our case, we need to find the cube of (2ab). We can start by rewriting the formula with the given values:
(2ab)^3 = (2ab)^3 + 3(2ab)^2(2ab) + 3(2ab)(2ab)^2 + (2ab)^3
Expanding the Expression
Let's expand each term:
- (2ab)^3 = 8a^3b^3 (since 2^3 = 8 and a^3b^3 means a cubed times b cubed)
- 3(2ab)^2(2ab) = 3(4a^2b^2)(2ab) = 24a^3b^3 (since 2^2 = 4 and 3 times 4 is 12)
- 3(2ab)(2ab)^2 = 3(2ab)(4a^2b^2) = 24a^3b^3 (similar to the previous step)
- (2ab)^3 = 8a^3b^3 (same as the first term)
Combining Like Terms
Now, let's combine the like terms:
(2ab)^3 = 8a^3b^3 + 24a^3b^3 + 24a^3b^3 + 8a^3b^3
Simplifying the Expression
Finally, we can simplify the expression by adding the coefficients:
(2ab)^3 = 64a^3b^3
And that's the answer!
