展开 (rcos(θ)+rsin(θ))^2

解答

展开

(r cos (θ) + r sin (θ))^{2}

r^{2} sin (2 θ) + r^{2}

求解步骤

(r cos (θ) + r sin (θ))^{2}

使用完全平方公式:

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

(r cos (θ) + r sin (θ))^{2} = (r cos (θ))^{2} + 2 r cos (θ) r sin (θ) + (r sin (θ))^{2}

= (r cos (θ))^{2} + 2 r cos (θ) r sin (θ) + (r sin (θ))^{2}

化简

(r cos (θ))^{2} + 2 r cos (θ) r sin (θ) + (r sin (θ))^{2} : r^{2} (sin (2 θ) + 1)

= r^{2} (sin (2 θ) + 1)

使用分配律:

a (b + c) = ab + a c

r^{2} (sin (2 θ) + 1) = r^{2} sin (2 θ) + r^{2} \cdot 1

= r^{2} sin (2 θ) + r^{2} \cdot 1

使用法则:

a \cdot 1 = a

r^{2} \cdot 1 = r^{2}

= r^{2} sin (2 θ) + r^{2}

s im pl i f y (v + \frac{1}{2}) (v - \frac{1}{2})

e x p an d (\frac{7}{3} a - b) (\frac{7}{3} a + b)

e x p an d - \frac{2 ( 7 + 1939 )}{15}

e x p an d \frac{( x + 9 ) ( x + 10 )}{x - 9}

e x p an d 19 sin (\frac{π}{6} (x + 3)) + 21