Question

Simplify the expression: x - 6x(8x^2 + 9) - (6x^3 - 7x).

Option 1: -46x^3 - 52x
Option 2: -54x^3 + x
Option 3: -54x^3 - 60x
Option 4: -46x^3 - 38x

Answer 1

To simplify the expression x - 6x(8x^2 + 9) - (6x^3 - 7x), distribute the terms and combine like terms to get -54x^3 - 46x.

Step-by-step explanation:

To simplify the expression x - 6x(8x^2 + 9) - (6x^3 - 7x), we can expand and distribute the terms:

x - 6x(8x^2 + 9) - (6x^3 - 7x) = x - 48x^3 - 54x - (6x^3 - 7x)

Next, combine like terms by adding and subtracting:

x - 48x^3 - 54x - (6x^3 - 7x) = x - 48x^3 - 54x - 6x^3 + 7x

Finally, simplify further by combining like terms:

x - 48x^3 - 54x - 6x^3 + 7x = -54x^3 - 46x

Simplification of an expression involves reducing or condensing it to a more concise or standard form while preserving its mathematical equivalence. This process often includes combining like terms, factoring, and applying mathematical operations to make the expression easier to work with or understand.

Therefore, the simplified expression is -54x^3 - 46x, which corresponds to option 3.