Question

simplify (a+b-2c)²+(b+c-2a)²-(c+a-2b)²+2(a+b-2c)(b+c-2a)​

Answer 1

Answer:

Step-by-step explanation

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

Let x= a+b-2c

Y=c+a-2c

Therefore

=x^2+y^2+2xy

=(x+y) ^2

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

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

Answer 2

Step-by-step Explanation:

By using the formula,

(x + y + z)² = x² + y² + z² + 2(xy + yz + xx)

The given questions is,

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

(a+b-2c)² = a² + b² + 4c² + 2a + 2b - 4c

(b+c-2a)² = 4a² + b² + c² - 4a + 2b + 2c

(c+a-2b)² = a² + 4b² + c² + 2a - 4b + 2c

2(a+b-2c)(b + c - 2a)= (2a + 2b - 4c)(b + c - 2a)

= 2ab + 2ac - 4a² + 2b² + 2bc - 4ab - 4bc -4c²+8ac

(a+b-2c)²+(b+c-2a)²-(c+a-2b)²+2(a+b-2c)(b+c-2a) =

a² + b² + 4c² + 2a + 2b - 4c + 4a² + b² + c² - 4a + 2b + 2c + a² + 4b² + c² + 2a - 4b + 2c + 2ab + 2ac - 4a² + 2b² + 2bc - 4ab - 4bc -4c²+8ac

= 2a² + 6b² - 2c² - 2(ab + bc - 4ac)