Question

Solve the expression (3√3x+1)^3.

a) 27(3x+1)
b) 27(3√3x+1)
c) 27(3√3x+1)^2
d) 27(9x^2 + 6√3x + 1)

Answer 1

To solve the expression (3√3x+1)³, we need to apply the rule for cubing a binomial. The correct option is d) 27(9x² + 6√3x + 1).

Step-by-step explanation:

To solve the expression (3√3x+1)³, we need to apply the rule for cubing a binomial. The rule states that (a + b)³ = a³ + 3a²b + 3ab² + b³. In this case, the binomial is 3√3x+1, so we have:

(3√3x+1)³ = (3√3x)³ + 3(3√3x)²(1) + 3(3√3x)(1)² + (1)³

Applying the rule, we simplify the expression:

(3√3x+1)³ = 27(3√3x)³ + 9(3√3x)² + 9(3√3x) + 1

Further simplifying, we have:

(3√3x+1)³ = 27(27x√3) + 9(9x) + 9(3√3x) + 1

Combining like terms:

(3√3x+1)³ = 729x√3 + 81x + 27√3x + 1

So, the correct option is d) 27(9x² + 6√3x + 1).