What is factor 6(x+6)^2(2x-5)-(x+6)(2x+5)^3 ?

The solution to factor 6(x+6)^2(2x-5)-(x+6)(2x+5)^3 is -(x+6)(8x^3+48x^2+108x+305)

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factor 6(x+6)^2(2x-5)-(x+6)(2x+5)^3

factor

6 (x + 6)^{2} (2 x - 5) - (x + 6) (2 x + 5)^{3}

- (x + 6) (8 x^{3} + 48 x^{2} + 108 x + 305)

Solution steps

6 (x + 6)^{2} (2 x - 5) - (x + 6) (2 x + 5)^{3}

Factor out common term

(x + 6) : (x + 6) (6 (x + 6) (2 x - 5) - (2 x + 5)^{3})

= (x + 6) (6 (x + 6) (2 x - 5) - (2 x + 5)^{3})

Expand

6 (x + 6) (2 x - 5) - (2 x + 5)^{3} : - 8 x^{3} - 48 x^{2} - 108 x - 305

= (x + 6) (- 8 x^{3} - 48 x^{2} - 108 x - 305)

Factor

- 8 x^{3} - 48 x^{2} - 108 x - 305 : - (8 x^{3} + 48 x^{2} + 108 x + 305)

= (x + 6) (- (8 x^{3} + 48 x^{2} + 108 x + 305))

Apply rule:

a (- b) = - ab

(x + 6) (- (8 x^{3} + 48 x^{2} + 108 x + 305)) = - (x + 6) (8 x^{3} + 48 x^{2} + 108 x + 305)

= - (x + 6) (8 x^{3} + 48 x^{2} + 108 x + 305)

\frac{1}{6} \cdot \frac{1}{6}

x - 21 = 6

\frac{15}{3} - \frac{4}{9} - \frac{1}{6} + \frac{11}{18} - \frac{1}{36} + 2

6 < (x^{2} + 72 x + 36) 7

\frac{2}{2} - \frac{1}{2}

What is factor 6(x+6)^2(2x-5)-(x+6)(2x+5)^3 ?
The solution to factor 6(x+6)^2(2x-5)-(x+6)(2x+5)^3 is -(x+6)(8x^3+48x^2+108x+305)