3x^3y + 12xy − 9x^2y − 36y Rewrite the expression completely factored. Show the steps of your work.

1 answer:

4 0

Factor 3 out of 12:
3x^3y + 3 • 4xy - 9x^2y - 36y

Factor out 3 out of -9:
3x^3y + 3(4xy) + 3 • -3x^2y - 36y

Factor 3 out of -36:
3(x^3y) + 3(4x7) + 3(-3x^2y) + 3(-12)y

Factor 3 out of 3 (x^3y) + 3(-12y):
3(x^2y + 4xy) + 3(-3x^2y) + 3(-12y)

Factor 3 out of 3 (x^3y + 4xy) + 3(-3x^2y):
3(x^2y + 4xy - 3x^2y) + 3(-12y)

Factor 3 out of
3 (x^3y + 4xy - 3x^2y) + 3 (-12y):
3 (x^3y + 4xy - 3x^2y - 12y)

You might be interested in

Will give brainlist or whatever.

max2010maxim [7]

Quarters and 1 dime

4 0

2 years ago

Please help!!

yarga [219]

Because this is a fourth degree that will be tricky to factor as it is, we will do a u substitution. Let $x^2=u$ . We can now rewrite that polynomial in terms of u: $u^2-7u-8=0$ . Filling into the quadratic formula we have $u=\frac{7+/-\sqrt{49-4(1)(-8)}}{2}$ . Simplifying down $u=\frac{7+/-\sqrt{81}}{2}$ and $u=\frac{7+9}{2}$ or $u=\frac{7-9}{2}$ . That means that u = 8 or u = -1. But don't forget that we let $u=x^2$ , so we have to put x-squared back in for u. That gives us $x^2=8$ which simplifies down to $+/-2\sqrt{2}$ . That also gives us $x^2=-1$ . When we take the square root of -1, we have to use the fact that -1 = i^2, so we sub that in to get $x=+/-i$ . All in all, your solutions are as follows: $2\sqrt{2},-2\sqrt{2},i,-i$ which is choice b.