Question

Factor 6x³y 6xy − 12x² − 12 completely. a. 6(xy − 2)(x² + 1) b. (6xy − 2)(x² + 1) c. 6(x³y + xy)(2x² − 2) d. (xy − 2)(x² + 1)

Answer 1

To factor the expression 6x³y + 6xy - 12x² - 12, we first pull out the common factor of 6, then rearrange terms to group like factors together, and finally factor out common factors to get 6(xy - 2)(x² + 1), which is option (a).

Step-by-step explanation:

To factor the expression 6x³y + 6xy − 12x² − 12 completely, we start by looking for common factors in all terms. The common factor that can be pulled out from each term is 6. This leaves us with:

6(x³y + xy - 2x² - 2)

Next, we look to see if there are any other factors that can be factored out. Since x is common in the first two terms and none in the last two, we rearrange the terms to group like factors together:

6((x³y + xy) - 2(x² + 1))

Now, factor out the common x from the first group:

6(xy(x² + 1) - 2(x² + 1))

Notice that (x² + 1) is a common factor in both groups. We can then factor this out:

6(x² + 1)(xy - 2)

Therefore, the completely factored form of the expression is 6(xy - 2)(x² + 1), which corresponds to option (a).