Question

Which expression in factored form is equivalent to this expression? 4(x² - 2x) - 2(x² - 3)

a. 2(x - 1)(2x + 3)
b. 2(x + 1)(2x - 3)
c. 4(x - 1)(x + 3)
d. 4(x + 1)(x - 3)

Answer 1

The expression in factored form that is equivalent to 4(x² - 2x) - 2(x² - 3) is 2(x - 1)(2x + 3) - 2x² + 6.

Step-by-step explanation:

To factor the expression 4(x² - 2x) - 2(x² - 3), we can start by factoring out the common factors from each term. Factoring out 4 and x from the first term, and -2 from the second term, we get:

4(x² - 2x) - 2(x² - 3) = 4x(x - 2) - 2(x² - 3)

Next, we can further simplify the expression:

4x(x - 2) - 2(x² - 3) = 4x(x - 2) - 2x² + 6

Finally, we can factor out a common factor from the last two terms:

4x(x - 2) - 2x² + 6 = 2(x - 1)(2x + 3) - 2x² + 6 = 2(x - 1)(2x + 3) - 2x² + 6 = 2(x - 1)(2x + 3) - 2x² + 6