Problem 54 - College Algebra

Question

Find each product. $$(3 x+4)^{3}$$

Step-by-Step Solution

Answer

The expanded form of the cubic binomial is \(27x^{3}+108x^{2}+192x+64\).

Step 1: Apply the Binomial Expansion formula

The cube of a binomial, (a+b)^3, can be expanded using the formula according to the binomial theorem. The formula is \(a^{3}+3a^{2}b+3ab^{2}+b^{3}\). Here, a=3x and b=4. Replace a and b in the formula with the values.

Step 2: Calculate the value for each term

After replacing a and b into the formula, you get \((3x)^{3}+3(3x)^{2}(4)+3(3x)(4)^{2}+4^{3}\). Calculate each term separately.

Step 3: Simplify the equation

After calculations, you will get 27x^{3}+108x^{2}+192x+64. Combine like terms, if any.