Question

Write (3x-1)^3 in the expanded form

Answer 1

Answer:

$(3x - 1)^{3} = (3x)^{3} - (1)^{3} - 3 \times (3x)^{2} + 3 \times (3x) \times ( - 1)^{2} \\ = 27 {x}^{3} - 1 - 27 {x}^{2} + 9x$

Answer 2

Answer:

$\Large\boxed{27x^3-27x^2+9x-1}$

Step-by-step explanation:

GIVEN:

(3x-1)³ (by using with perfect cube formula.)

You can also used distributive property.

SOLUTIONS:

First, used perfect cube formula.

$\Large\boxed{\textnormal{PERFECT CUBE FORMULA}}$

$\displaystyle (A-B)^3=A^3-3A^2B+3AB^2-B^3$

A=3x

B=1

Rewrite the problem down.

$\displaystyle (3x)^3-3(3x)^2*1+3*3x*1^2-1^3$

Solve. (Simplify/ to find the answer!)

$\Large\boxed{\textnormal{APPLY RULE!}}$

$\displaystyle 1^a=1$

$\displaystyle 1^2=1,\:1^3=1$

$\displaystyle \left(3x\right)^3-3*\:1\* \left(3x\right)^2+3* \:3*\:1* \:x-1$

$\displaystyle 3^3=3*3*3=27$

$\displaystyle 3*3*1=9$

$\Large\boxed{27x^3-27x^2+9x-1}$

As a result, the final answer is 27x³-27x²+9x-1.