Factor completely write without negative exponents 8x253 x1

Factor completely ; write without negative exponents

8(x^2+5)^-3 (x-1)^3 - 3(2x)(x-1)^4(x^2+5)^-4

show steps please

Solution

8(x²+5)^-3 (x-1)³ - 3(2x)(x-1)⁴(x²+5)^-4

formula :a^-m=1/a^m

(8((x-1)³/(x²+5)³))- (3(2x)(x-1)⁴/(x²+5)⁴)

=[(8((x-1)³(x²+5)) - (3(2x)(x-1)⁴)]/(x²+5)⁴

=[(8(x²+5) - (3(2x)(x-1))] [(x-1)³/(x²+5)⁴]

=[(8x²+40) - (6x²-6x)] [(x-1)³/(x²+5)⁴]

=[2x²+6x+40)] [(x-1)³/(x²+5)⁴]

=2[x²+3x+20)] [(x-1)³/(x²+5)⁴]