展开 (2-4cos(x))^2

解答

展开

(2 - 4 cos (x))^{2}

4 - 16 cos (x) + 16 cos^{2} (x)

求解步骤

(2 - 4 cos (x))^{2}

使用完全平方公式:

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

(2 - 4 cos (x))^{2} = 2^{2} - 2 \cdot 2 \cdot 4 cos (x) + (4 cos (x))^{2}

= 2^{2} - 2 \cdot 2 \cdot 4 cos (x) + (4 cos (x))^{2}

化简

2^{2} - 2 \cdot 2 \cdot 4 cos (x) + (4 cos (x))^{2} : 4 - 16 cos (x) + 16 cos^{2} (x)

= 4 - 16 cos (x) + 16 cos^{2} (x)

e x p an d 3 X^{2} + 1 X - 2

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

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

e x p an d \frac{( 2 x ^{4} - 6 x ^{2} )}{( x ^{2} - 1 ) ^{2}}

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