확장 (A+(Ccos(y))+(Dcos(z))-(B*cos(x)))^2

해법

확장

(A + (C \cdot cos (y)) + (D \cdot cos (z)) - (B \cdot cos (x)))^{2}

A^{2} + C^{2} cos^{2} (y) + D^{2} cos^{2} (z) + B^{2} cos^{2} (x) + 2 A C cos (y) + 2 A D cos (z) - 2 A B cos (x) + C D cos (y) cos (z) - CB cos (y) cos (x) + C D cos (z) cos (y) - D B cos (z) cos (x) - CB cos (x) cos (y) - D B cos (x) cos (z)

솔루션 단계

(A + (C cos (y)) + (D cos (z)) - (B cos (x)))^{2}

A + (C cos (y)) + (D cos (z)) - (B cos (x))

간소화하다 :

A + C cos (y) + D cos (z) - B cos (x)

= (A + C cos (y) + D cos (z) - B cos (x))^{2}

지수 규칙 적용:

a^{b + c} = a^{b} \cdot a^{c}

(A + C cos (y) + D cos (z) - B cos (x))^{2} = (A + C cos (y) + D cos (z) - B cos (x)) (A + C cos (y) + D cos (z) - B cos (x))

= (A + C cos (y) + D cos (z) - B cos (x)) (A + C cos (y) + D cos (z) - B cos (x))

괄호 배포

= AA + A C cos (y) + A D cos (z) + A (- B cos (x)) + C cos (y) A + C cos (y) C cos (y) + C cos (y) D cos (z) + C cos (y) (- B cos (x)) + D cos (z) A + D cos (z) C cos (y) + D cos (z) D cos (z) + D cos (z) (- B cos (x)) - B cos (x) A - B cos (x) C cos (y) - B cos (x) D cos (z) - B cos (x) (- B cos (x))

AA + A C cos (y) + A D cos (z) + A (- B cos (x)) + C cos (y) A + C cos (y) C cos (y) + C cos (y) D cos (z) + C cos (y) (- B cos (x)) + D cos (z) A + D cos (z) C cos (y) + D cos (z) D cos (z) + D cos (z) (- B cos (x)) - B cos (x) A - B cos (x) C cos (y) - B cos (x) D cos (z) - B cos (x) (- B cos (x))

간소화하다 :

A^{2} + C^{2} cos^{2} (y) + D^{2} cos^{2} (z) + B^{2} cos^{2} (x) + 2 A C cos (y) + 2 A D cos (z) - 2 A B cos (x) + C D cos (y) cos (z) - CB cos (y) cos (x) + C D cos (z) cos (y) - D B cos (z) cos (x) - CB cos (x) cos (y) - D B cos (x) cos (z)

= A^{2} + C^{2} cos^{2} (y) + D^{2} cos^{2} (z) + B^{2} cos^{2} (x) + 2 A C cos (y) + 2 A D cos (z) - 2 A B cos (x) + C D cos (y) cos (z) - CB cos (y) cos (x) + C D cos (z) cos (y) - D B cos (z) cos (x) - CB cos (x) cos (y) - D B cos (x) cos (z)