Question

write 3 X + 1 the whole cube in the expanded form​

Answer 1

Answer:

${(3x + 1)}^{3}$

${(3x)}^{3} + {(1)}^{3} + 3 \times 3x \times 1(3x + 1)$

${27x}^{3} + 1 + 9x(3x + 1)$

${27x}^{3} + 1 + {27x}^{2} + 9x$

This can be written as

${27x}^{3} + {27x}^{2} + 9x + 1$

Answer 2

Given,

(3x+1)³

To find,

The expanded form of (3x+1)³.

Solution,

The expanded form of (3x+1)³ will be 27x³ + 27x² + 9x + 1.

We can easily solve this problem by following the given steps.

Now, if we carefully observe the given expression, we find that the identity, (a+b)³, is to be used to expand the expression.

(a+b)³ = a³+b³+3ab(a+b)

In this case, we have a = 3x and b = 1.

Using the identity (a+b)³, we get

(3x+1)³ = (3x)³+(1)³+3×3x×1(3x+1)

(3x+1)³ = 27x³ + 1 + 9x(3x+1) [ Solving the cubes and multiplying 3×3x×1]

(3x+1)³ = 27x³ + 1 + 27x² + 9x [ Multiplying 9x into the bracket]

(3x+1)³ = 27x³ + 27x² + 9x + 1

( This can not be solved further because the variables are different for each term.)

Hence, the expanded form of (3x+1)³ is 27x³ + 27x² + 9x + 1.