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受欢迎的代数 >

展开 ,(x+3)^4(x-2)(x+6)^3

解答

展开

(x + 3)^{4} (x - 2) (x + 6)^{3}

解答

x^{8} + 28 x^{7} + 318 x^{6} + 1836 x^{5} + 5265 x^{4} + 3888 x^{3} - 17496 x^{2} - 46656 x - 34992

求解步骤

(x + 3)^{4} (x - 2) (x + 6)^{3}

= (x + 3)^{4} (x + 6)^{3} (x - 2)

展开

(x + 6)^{3} : x^{3} + 18 x^{2} + 108 x + 216

= (x + 3)^{4} (x^{3} + 18 x^{2} + 108 x + 216) (x - 2)

展开

(x + 3)^{4} (x - 2) : x (x + 3)^{4} - 2 (x + 3)^{4}

= (x (x + 3)^{4} - 2 (x + 3)^{4}) (x^{3} + 18 x^{2} + 108 x + 216)

打开括号

= x (x + 3)^{4} x^{3} + x (x + 3)^{4} \cdot 18 x^{2} + x (x + 3)^{4} \cdot 108 x + x (x + 3)^{4} \cdot 216 - 2 (x + 3)^{4} x^{3} - 2 (x + 3)^{4} \cdot 18 x^{2} - 2 (x + 3)^{4} \cdot 108 x - 2 (x + 3)^{4} \cdot 216

化简

x (x + 3)^{4} x^{3} + x (x + 3)^{4} \cdot 18 x^{2} + x (x + 3)^{4} \cdot 108 x + x (x + 3)^{4} \cdot 216 - 2 (x + 3)^{4} x^{3} - 2 (x + 3)^{4} \cdot 18 x^{2} - 2 (x + 3)^{4} \cdot 108 x - 2 (x + 3)^{4} \cdot 216 : x^{4} (x + 3)^{4} - 432 (x + 3)^{4} + 16 x^{3} (x + 3)^{4} + 72 x^{2} (x + 3)^{4}

= x^{4} (x + 3)^{4} - 432 (x + 3)^{4} + 16 x^{3} (x + 3)^{4} + 72 x^{2} (x + 3)^{4}

展开

x^{4} (x + 3)^{4} : x^{8} + 12 x^{7} + 54 x^{6} + 108 x^{5} + 81 x^{4}

= x^{8} + 12 x^{7} + 54 x^{6} + 108 x^{5} + 81 x^{4} - 432 (x + 3)^{4} + 16 x^{3} (x + 3)^{4} + 72 x^{2} (x + 3)^{4}

展开

- 432 (x + 3)^{4} : - 432 x^{4} - 5184 x^{3} - 23328 x^{2} - 46656 x - 34992

= x^{8} + 12 x^{7} + 54 x^{6} + 108 x^{5} + 81 x^{4} - 432 x^{4} - 5184 x^{3} - 23328 x^{2} - 46656 x - 34992 + 16 x^{3} (x + 3)^{4} + 72 x^{2} (x + 3)^{4}

展开

16 x^{3} (x + 3)^{4} : 16 x^{7} + 192 x^{6} + 864 x^{5} + 1728 x^{4} + 1296 x^{3}

= x^{8} + 12 x^{7} + 54 x^{6} + 108 x^{5} + 81 x^{4} - 432 x^{4} - 5184 x^{3} - 23328 x^{2} - 46656 x - 34992 + 16 x^{7} + 192 x^{6} + 864 x^{5} + 1728 x^{4} + 1296 x^{3} + 72 x^{2} (x + 3)^{4}

展开

72 x^{2} (x + 3)^{4} : 72 x^{6} + 864 x^{5} + 3888 x^{4} + 7776 x^{3} + 5832 x^{2}

= x^{8} + 12 x^{7} + 54 x^{6} + 108 x^{5} + 81 x^{4} - 432 x^{4} - 5184 x^{3} - 23328 x^{2} - 46656 x - 34992 + 16 x^{7} + 192 x^{6} + 864 x^{5} + 1728 x^{4} + 1296 x^{3} + 72 x^{6} + 864 x^{5} + 3888 x^{4} + 7776 x^{3} + 5832 x^{2}

化简

x^{8} + 12 x^{7} + 54 x^{6} + 108 x^{5} + 81 x^{4} - 432 x^{4} - 5184 x^{3} - 23328 x^{2} - 46656 x - 34992 + 16 x^{7} + 192 x^{6} + 864 x^{5} + 1728 x^{4} + 1296 x^{3} + 72 x^{6} + 864 x^{5} + 3888 x^{4} + 7776 x^{3} + 5832 x^{2} : x^{8} + 28 x^{7} + 318 x^{6} + 1836 x^{5} + 5265 x^{4} + 3888 x^{3} - 17496 x^{2} - 46656 x - 34992

= x^{8} + 28 x^{7} + 318 x^{6} + 1836 x^{5} + 5265 x^{4} + 3888 x^{3} - 17496 x^{2} - 46656 x - 34992

流行的例子

展开 sin((x+1)^2)

e x p an d sin ((x + 1)^{2})

展开 ((-2-3t)^2)/(36)

e x p an d \frac{( - 2 - 3 t ) ^{2}}{36}

展开-12*(x-1)*((x-1)/3)

e x p an d - 12 \cdot (x - 1) \cdot (\frac{x - 1}{3})

展开 (12x+69)/((2x^2+5)(x+6))

e x p an d \frac{12 x + 69}{( 2 x ^{2} + 5 ) ( x + 6 )}

化简-6(x/(10)-y)

s im pl i f y - 6 (\frac{x}{10} - y)