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受欢迎的代数 >

化简 15(a-b+c)^2+(b-c+a)^2+2(a-b+c)(b-c+a)

解答

化简

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

解答

15 (a - b + c)^{2} - b^{2} + 3 a^{2} + 2 b c + 2 ab - c^{2} - 2 a c

求解步骤

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

展开

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

= 15 (a - b + c)^{2} + b^{2} - 2 b c + 2 ab + c^{2} + a^{2} - 2 a c + 2 (a - b + c) (b - c + a)

展开

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

= 15 (a - b + c)^{2} + b^{2} - 2 b c + 2 ab + c^{2} + a^{2} - 2 a c + 2 a^{2} - 2 b^{2} + 4 b c - 2 c^{2}

对同类项分组

= 15 (a - b + c)^{2} + b^{2} - 2 b^{2} + 2 a^{2} + a^{2} - 2 b c + 4 b c + 2 ab + c^{2} - 2 c^{2} - 2 a c

同类项相加:

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

= 15 (a - b + c)^{2} - b^{2} + 2 a^{2} + a^{2} - 2 b c + 4 b c + 2 ab + c^{2} - 2 c^{2} - 2 a c

同类项相加:

2 a^{2} + a^{2} = 3 a^{2}

= 15 (a - b + c)^{2} - b^{2} + 3 a^{2} - 2 b c + 4 b c + 2 ab + c^{2} - 2 c^{2} - 2 a c

同类项相加:

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

= 15 (a - b + c)^{2} - b^{2} + 3 a^{2} + 2 b c + 2 ab + c^{2} - 2 c^{2} - 2 a c

同类项相加:

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

= 15 (a - b + c)^{2} - b^{2} + 3 a^{2} + 2 b c + 2 ab - c^{2} - 2 a c

流行的例子

化简 ((x)1)/((log_{x)(7))}

s im pl i f y \frac{( x ) 1}{( lo g _{x} ( 7 ) )}

化简 (z^2)^{-1}0

s im pl i f y (z^{2})^{- 1} 0

化简 3(2x-3)2(x+5)-1

s im pl i f y 3 (2 x - 3) 2 (x + 5) - 1

化简 (a/2+2/a)^2

s im pl i f y (\frac{a}{2} + \frac{2}{a})^{2}

因式分解 64x^2y^2-121z^2

f a c t or 64 x^{2} y^{2} - 121 z^{2}