Determine the cube of the expression by writing the expression as the square of an expression multiplied by another
expression.
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Question

Quizplus · Accepted Answer

We can write 11ebb63d_1b9e_6dc0_b851_092d3a7ebd2a_TB8475_11 as (11ebb63d_1b9e_6dc0_b851_092d3a7ebd2a_TB8475_11)^(2/3) * (11ebb63d_1b9e_6dc0_b851_092d3a7ebd2a_TB8475_11)^(1/3). Taking the cube of this expression, we get (11ebb63d_1b9e_6dc0_b851_092d3a7ebd2a_TB8475_11)^(2/3) * (11ebb63d_1b9e_6dc0_b851_092d3a7ebd2a_TB8475_11)^(1/3) * (11ebb63d_1b9e_6dc0_b851_092d3a7ebd2a_TB8475_11)^(1/3) = 11ebb63d_1b9e_6dc3_b851_6f568bb7b6f7_TB8475_11. Therefore, the answer is C. To determine the cube of the expression by writing the expression as the square of an expression multiplied by another expression, we can use the formula: 
(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3

Let's say our expression is x. 
Then, we can write: 
x^3 = (x^2) * x 
To use the formula above, we need to express x^2 as (a + b)^2. 
Notice that (2x)(-3x) = -6x^2 and (-3x)^2 = 9x^2. 
So we can write: 
(x^2) = (2x - 3x)^2 = (2x)^2 - 2(2x)(3x) + (3x)^2 = 4x^2 - 12x^2 + 9x^2 = x^2

Now we have: 
x^3 = x^2 * x = (x^2) * x = (2x - 3x + x) * x^2 = 0 * x^2 = 0

Therefore, the answer is option C: 11ebb63d_1b9e_6dc3_b851_6f568bb7b6f7_TB8475_11.

Determine the Cube of the Expression by Writing the Expression