因式分解 343sin^3(x)+1000

解答

因式分解

343 sin^{3} (x) + 1000

(7 sin (x) + 10) (49 sin^{2} (x) - 70 sin (x) + 100)

求解步骤

343 sin^{3} (x) + 1000

将

343 sin^{3} (x) + 1000

改写为

(7 sin (x))^{3} + 1 0^{3}

= (7 sin (x))^{3} + 1 0^{3}

使用立方和公式:

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

(7 sin (x))^{3} + 1 0^{3} = (7 sin (x) + 10) (7^{2} sin^{2} (x) - 10 \cdot 7 sin (x) + 1 0^{2})

= (7 sin (x) + 10) (7^{2} sin^{2} (x) - 10 \cdot 7 sin (x) + 1 0^{2})

整理后得

= (7 sin (x) + 10) (49 sin^{2} (x) - 70 sin (x) + 100)

f a c t or (a + b)^{2} - (a + b) - 6

f a c t or 15 x + 18 x

f a c t or 4^{2} + 4^{2} + 4^{2} + 4^{2}

f a c t or (6 x - 6) + h

\frac{d}{d t} ((s) (6 sin (2 t)))