因式分解 4d^3+16de^2-20df^3

解答

因式分解

4 d^{3} + 16 d e^{2} - 20 d f^{3}

4 d (d^{2} + 4 e^{2} - 5 f^{3})

求解步骤

4 d^{3} + 16 d e^{2} - 20 d f^{3}

使用指数法则:

a^{b + c} = a^{b} a^{c}

d^{3} = d d^{2}

= 4 d d^{2} + 16 e^{2} d - 20 d f^{3}

因式分解出通项

d

= d (4 d^{2} + 16 e^{2} - 20 f^{3})

分解

4 d^{2} + 16 e^{2} - 20 f^{3} : 4 (d^{2} + 4 e^{2} - 5 f^{3})

= 4 d (d^{2} + 4 e^{2} - 5 f^{3})

f (x) = (cos (3 x))^{2}

f a c t or a x + a c - b x - b c

s im pl i f y [3.5]

f a c t or 21 uv + 8 b + 3 u + 56 b v

f a c t or cos^{3} (x) + sin^{3} (x)