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受欢迎的代数 >

化简 (a+b-c)^2-(a-b+c)^2-2*(b-c)^2

解答

化简

(a + b - c)^{2} - (a - b + c)^{2} - 2 \cdot (b - c)^{2}

解答

4 ab - 4 a c - 2 b^{2} + 4 b c - 2 c^{2}

求解步骤

(a + b - c)^{2} - (a - b + c)^{2} - 2 (b - c)^{2}

展开

(a + b - c)^{2} : a^{2} + 2 ab - 2 a c + b^{2} - 2 b c + c^{2}

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

展开

- (a - b + c)^{2} : - a^{2} + 2 ab - 2 a c - b^{2} + 2 b c - c^{2}

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

展开

- 2 (b - c)^{2} : - 2 b^{2} + 4 b c - 2 c^{2}

= a^{2} + 2 ab - 2 a c + b^{2} - 2 b c + c^{2} - a^{2} + 2 ab - 2 a c - b^{2} + 2 b c - c^{2} - 2 b^{2} + 4 b c - 2 c^{2}

对同类项分组

= a^{2} - a^{2} + 2 ab + 2 ab - 2 a c - 2 a c + b^{2} - b^{2} - 2 b^{2} - 2 b c + 2 b c + 4 b c + c^{2} - c^{2} - 2 c^{2}

同类项相加:

a^{2} - a^{2} = 0

= 2 ab + 2 ab - 2 a c - 2 a c + b^{2} - b^{2} - 2 b^{2} - 2 b c + 2 b c + 4 b c + c^{2} - c^{2} - 2 c^{2}

同类项相加:

2 ab + 2 ab = 4 ab

= 4 ab - 2 a c - 2 a c + b^{2} - b^{2} - 2 b^{2} - 2 b c + 2 b c + 4 b c + c^{2} - c^{2} - 2 c^{2}

同类项相加:

- 2 a c - 2 a c = - 4 a c

= 4 ab - 4 a c + b^{2} - b^{2} - 2 b^{2} - 2 b c + 2 b c + 4 b c + c^{2} - c^{2} - 2 c^{2}

同类项相加:

b^{2} - b^{2} - 2 b^{2} = - 2 b^{2}

= 4 ab - 4 a c - 2 b^{2} - 2 b c + 2 b c + 4 b c + c^{2} - c^{2} - 2 c^{2}

同类项相加:

- 2 b c + 2 b c + 4 b c = 4 b c

= 4 ab - 4 a c - 2 b^{2} + 4 b c + c^{2} - c^{2} - 2 c^{2}

同类项相加:

c^{2} - c^{2} - 2 c^{2} = - 2 c^{2}

= 4 ab - 4 a c - 2 b^{2} + 4 b c - 2 c^{2}

流行的例子

化简 (2s+1)(2s+9)-(2s)^2

s im pl i f y (2 s + 1) (2 s + 9) - (2 s)^{2}

化简 2 x/3-3 x/8-7/12

s im pl i f y 2 \frac{x}{3} - 3 \frac{x}{8} - \frac{7}{12}

化简 ((10x^3*y^5))/((2x^2*y))

s im pl i f y \frac{( 10 x ^{3} \cdot y ^{5} )}{( 2 x ^{2} \cdot y )}

化简-(11)/a*b/3

s im pl i f y - \frac{11}{a} \cdot \frac{b}{3}

展开-4xy^3(5x^2+8y)

e x p an d - 4 x y^{3} (5 x^{2} + 8 y)