확장 (1+ce^{-(x^2)/2})^2

해법

확장

(1 + c e^{- \frac{x ^{2}}{2}})^{2}

1 + 2 c e^{- \frac{x ^{2}}{2}} + c^{2} e^{- x^{2}}

솔루션 단계

(1 + c e^{- \frac{x ^{2}}{2}})^{2}

완벽한 정사각형 공식 적용:

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

a = 1, b = c e^{- \frac{x ^{2}}{2}}

= 1^{2} + 2 \cdot 1 \cdot c e^{- \frac{x ^{2}}{2}} + (c e^{- \frac{x ^{2}}{2}})^{2}

1^{2} + 2 \cdot 1 \cdot c e^{- \frac{x ^{2}}{2}} + (c e^{- \frac{x ^{2}}{2}})^{2}

단순화하세요:

1 + 2 c e^{- \frac{x ^{2}}{2}} + c^{2} e^{- x^{2}}

= 1 + 2 c e^{- \frac{x ^{2}}{2}} + c^{2} e^{- x^{2}}