Which expression is the simplest form -(4x^3+x^2)+2(x^3-3x^2)

6x^3-5x^2

Step-by-step explanation:

(4x^3+x^2)+2(x^3-3x^2)

4x^3+x^2+2x^3-6x^2

4x^3+2x^3+x^2-6x^2

6x^3+x^2-6x^2

6x^3-5x^2

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4