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受欢迎的代数 >

展开 sqrt(1+4x^2(x^2-1))

解答

展开

1 + 4 x^{2} (x^{2} - 1)

解答

2 x^{2} - 1

求解步骤

1 + 4 x^{2} (x^{2} - 1)

乘开

1 + 4 x^{2} (x^{2} - 1) : 1 + 4 x^{4} - 4 x^{2}

= 1 + 4 x^{4} - 4 x^{2}

分解

4 x^{4} - 4 x^{2} + 1 : (2 x + 1)^{2} (2 x - 1)^{2}

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

使用根式运算法则:

n ab = n a n b,

假定

a \geq 0, b \geq 0

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

使用根式运算法则:

n a^{n} = a,

假定

a \geq 0

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

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

使用根式运算法则:

n a^{n} = a,

假定

a \geq 0

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

= (2 x + 1) (2 x - 1)

使用平方差公式:

(a + b) (a - b) = a^{2} - b^{2}

a = 2 x, b = 1

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

化简

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

= 2 x^{2} - 1

流行的例子

展开 ln(\sqrt[3]{uvw})

e x p an d ln (3 uv w)

展开 2-4(1-3x=82)

e x p an d 2 - 4 (1 - 3 x = 82)

展开 (8,-6)x(2,-15)

e x p an d (8, - 6) x (2, - 15)

展开 (5x-1)/((x+1)(1+x+3x^2))

e x p an d \frac{5 x - 1}{( x + 1 ) ( 1 + x + 3 x ^{2} )}

展开 x/((3x^2+2)(6+3x^2t+2t))

e x p an d \frac{x}{( 3 x ^{2} + 2 ) ( 6 + 3 x ^{2} t + 2 t )}