因式分解 2x^2(x+1)^2-x^2(x+1)^3(x-3)

解答

因式分解

2 x^{2} (x + 1)^{2} - x^{2} (x + 1)^{3} (x - 3)

x^{2} (x + 1)^{2} (- x^{2} + 2 x + 5)

求解步骤

2 x^{2} (x + 1)^{2} - x^{2} (x + 1)^{3} (x - 3)

因式分解出通项

x^{2} (x + 1)^{2} : x^{2} (x + 1)^{2} (2 - (x + 1) (x - 3))

= x^{2} (x + 1)^{2} (2 - (x + 1) (x - 3))

展开

2 - (x + 1) (x - 3) : - x^{2} + 2 x + 5

= x^{2} (x + 1)^{2} (- x^{2} + 2 x + 5)

s im pl i f y (4)^{\frac{1}{2}}

f a c t or 2 x^{3} - 9 x^{2} + 7 x + 6

f a c t or 25 m^{100} - 12 1^{16}

\frac{9 x - 2}{5} = 2 x - 2

7 k^{2} + 37 k - 30 = 0