展开 ((2+cos(u)sin(u)))^2

解答

展开

((2 + cos (u) sin (u)))^{2}

4 + 4 cos (u) sin (u) + cos^{2} (u) sin^{2} (u)

求解步骤

(2 + cos (u) sin (u))^{2}

化简

(2 + cos (u) sin (u)) : 2 + cos (u) sin (u)

= (2 + cos (u) sin (u))^{2}

使用完全平方公式:

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

(2 + cos (u) sin (u))^{2} = 2^{2} + 2 \cdot 2 cos (u) sin (u) + (cos (u) sin (u))^{2}

= 2^{2} + 2 \cdot 2 cos (u) sin (u) + (cos (u) sin (u))^{2}

化简

2^{2} + 2 \cdot 2 cos (u) sin (u) + (cos (u) sin (u))^{2} : 4 + 4 cos (u) sin (u) + cos^{2} (u) sin^{2} (u)

= 4 + 4 cos (u) sin (u) + cos^{2} (u) sin^{2} (u)

e x p an d \frac{10 x + 9}{3 ( x + 1 ) ( 2 x + 3 )}

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

e x p an d \frac{4 x + 2}{( x - 2 ) ( 3 x + 4 )}

e x p an d (3 x - 3 c)^{3}

e x p an d 4 (y^{4} + 3 y^{2}) + 1