Question

If (x) and (n) are positive integers, which of the following is equivalent to (2x)³ - (2x)² ?

1) (2x)²
2) 2²(x³ - x²)
3) (2x)²[(2x)² -1]
4) (2x)²(4x² -1)
5) (2x)²[(2x)³ -1]

Answer 1

The expression (2x)³ - (2x)² is equivalent to (2x)²(4x² -1), which is found by factoring out the common term (2x)² and simplifying the terms within the parentheses.

Step-by-step explanation:

The question asks which of the following is equivalent to (2x)³ - (2x)². To find the equivalent expression, factor out the common term from the original expression. We take (2x)² as the common term, and we have:

(2x)²((2x) - 1)

Then expand the term (2x) to get 2² * x. This gives us:

(2x)²(2²x - 1)

This is equivalent to:

(2x)²(4x - 1)

Therefore, the correct answer is option 4: (2x)²(4x² -1).