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

化简

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

= - r^{2} sin (2 θ) + r^{2}

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s im pl i f y (4 - 14 - x) (4 + 14 - x)

s im pl i f y (2 x + 3 + 2)^{2}

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