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simplificar (a+b-c)^2+(a-b-c)^2-2(b-c)

Solução

simplificar

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

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

Passos da solução

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

Expandir

(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)

Expandir

(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)

Expandir

- 2 (b - c) : - 2 b + 2 c

= 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 c

Agrupar termos semelhantes

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

Somar elementos similares:

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

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

Somar elementos similares:

2 ab - 2 ab = 0

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

Somar elementos similares:

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

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

Somar elementos similares:

b^{2} + b^{2} = 2 b^{2}

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

Somar elementos similares:

- 2 b c + 2 b c = 0

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

Somar elementos similares:

c^{2} + c^{2} = 2 c^{2}

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

f a c t or 36 j^{2} - 100 k

e x p an d (3 q + b)^{3}

s im pl i f y (- x^{3} y^{2} z) (2 x^{3} y^{4} z)^{3}

s im pl i f y \frac{1}{( a ^{2} \cdot e ^{x} + e ^{- x} )}

s im pl i f y 8 p^{3} + \frac{12}{5} p^{2} + \frac{6}{25} p + \frac{1}{125}