x 672 36x 632 Help me to factor the exressionSolutionx 672 3

(x 6)^7/2 36(x 6)^3/2

^{Help me to factor the ex[ression}

Solution

(x 6)^7/2 36(x 6)^3/2

taking the gcf out of the expression

(x-6)^3/2 is the gcf of the expression

(x-6)^3/2 { ( x-3)^2 - 36 )}

(x-6)^3/2 { ( x^2 -6x + 9 - 36 )}

(x-6)^3/2 { ( x^2 -6x - 27 ) }

factoring x^2 -6x-27 we get

(x-6)^3/2 ( x-9) (x+3) = (x-6)(x-6)^1/2(x-9)(x-3)