• Step 1: Rewrite the cube as the product of three factors, each of which is the original binomial squared.




• (3a 4b)^3 = (3a 4b)(3a 4b)(3a 4b)





• Step 2: Multiply the first two factors using FOIL (first, outside, inside, last).




• (3a 4b)(3a 4b) = 9a^2 + 24ab + 16b^2





• Step 3: Multiply the result from Step 2 with the third factor.




• (9a^2 + 24ab + 16b^2)(3a 4b) = 27a^3 + 108a^2b + 144ab^2 + 64b^3

To expand the given cube, we need to multiply the given binomial with itself three times. However, instead of multiplying it directly, we can simplify the process by breaking it down into smaller steps.

In the first step, we rewrite the cube as the product of three factors, each of which is the original binomial squared. Then, in the second step, we use the FOIL method to multiply the first two factors. This gives us a quadratic expression in terms of a and b. Finally, in the third step, we multiply the result from Step 2 with the third factor, which is the original binomial. We distribute the terms and simplify the expression to get the expanded form of the given cube.

In conclusion, by following the above steps, we can easily expand any binomial cube and simplify it to obtain the expanded form.

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