Choose the correct simplification of the expression (7x - 3)(4x² - 3x - 6).
28x³ - 33x² - 33x - 18
28x³ + 33x² - 33x + 18
28x³ - 51x² - 33x + 18
28x³ - 33x² - 33x + 18

Solution:

Given, the expression is (7x - 3)(4x² - 3x - 6).

We have to simplify the given expression.

(7x - 3)(4x² - 3x - 6) = 7x(4x² - 3x - 6) - 3(4x² - 3x - 6)

= [7x(4x²) - 7x(3x) - 7x(6)] - [3(4x²) - 3(3x) - 3(6)]

= [28x³ - 21x² - 42x] - [12x² - 9x - 18]

= 28x³ - 21x² - 42x - 12x² + 9x + 18

By grouping of common terms,

= 28x³ - 21x² - 12x² - 42x + 9x + 18

= 28x³ + (-21 - 12)x² + (-42 + 9)x + 18

= 28x³ - 33x² - 33x + 18

Therefore, the simplified expression is 28x³ - 33x² - 33x + 18.

Choose the correct simplification of the expression (7x - 3)(4x² - 3x - 6)

Summary:

28x³ - 33x² - 33x + 18 is the correct simplification of the expression (7x - 3)(4x² - 3x - 6).