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受欢迎的代数 >

因式分解 sin^{22}(a)+cos^{22}(a)

解答

因式分解

sin^{22} (a) + cos^{22} (a)

解答

(sin^{2} (a) + cos^{2} (a)) (sin^{20} (a) - sin^{18} (a) cos^{2} (a) + sin^{16} (a) cos^{4} (a) - sin^{14} (a) cos^{6} (a) + sin^{12} (a) cos^{8} (a) - cos^{10} (a) sin^{10} (a) + cos^{12} (a) sin^{8} (a) - cos^{14} (a) sin^{6} (a) + cos^{16} (a) sin^{4} (a) - cos^{18} (a) sin^{2} (a) + cos^{20} (a))

求解步骤

sin^{22} (a) + cos^{22} (a)

将

sin^{22} (a) + cos^{22} (a)

改写为

(sin^{2} (a))^{11} + (cos^{2} (a))^{11}

= (sin^{2} (a))^{11} + (cos^{2} (a))^{11}

使用因式分解法则

x^{n} + y^{n} = (x + y) (x^{n - 1} - x^{n - 2} y + \dots - x y^{n - 2} + y^{n - 1})

n is odd

(sin^{2} (a))^{11} + (cos^{2} (a))^{11} = (sin^{2} (a) + cos^{2} (a)) (sin^{20} (a) - cos^{2} (a) sin^{18} (a) + cos^{4} (a) sin^{16} (a) - cos^{6} (a) sin^{14} (a) + cos^{8} (a) sin^{12} (a) - cos^{10} (a) sin^{10} (a) + cos^{12} (a) sin^{8} (a) - cos^{14} (a) sin^{6} (a) + cos^{16} (a) sin^{4} (a) - cos^{18} (a) sin^{2} (a) + cos^{20} (a))

= (sin^{2} (a) + cos^{2} (a)) (sin^{20} (a) - cos^{2} (a) sin^{18} (a) + cos^{4} (a) sin^{16} (a) - cos^{6} (a) sin^{14} (a) + cos^{8} (a) sin^{12} (a) - cos^{10} (a) sin^{10} (a) + cos^{12} (a) sin^{8} (a) - cos^{14} (a) sin^{6} (a) + cos^{16} (a) sin^{4} (a) - cos^{18} (a) sin^{2} (a) + cos^{20} (a))

流行的例子

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f a c t or (4 x^{10}) - (4 x^{5}) + 1

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f a c t or 8^{3} + 2 7^{3}

s im pl i f y \cdot + 5

因式分解 4x^2+7-3

f a c t or 4 x^{2} + 7 - 3

因式分解 2x-3y+(-5)

f a c t or 2 x - 3 y + (- 5)