Factor completely

Question

Factor completely. 12x^3(y+6)−28x^2(−6−y)−8x(y+6) Enter the factors. Enter the original expression if it cannot be factored.

Answer 1

12x³(y + 6) − 28x²(−6 − y) − 8x(y + 6)

 

We can start by distributing that negative sign in the middle part to the inside, essentially multiplying it by -1:

12x³(y + 6) + 28x²(6 + y) − 8x(y + 6)

 

Now that all three terms have a y+6, we can factor that out:

(y + 6)(12x³ + 28x² - 8x)

 

12, 28, and 8 all have a 4 in common, so:

4(y + 6)(3x³ + 7x² - 2x)

 

Each term also has an x in it, so we can factor that out as well:

4x(y + 6)(3x² + 7x - 2)

 

And now all the terms are factored out.