Question

(7a+b–c+d)²+(d-b-5a+c)²+2(7a+d+b-c)(c+d-b-5a) express as a perfect square​

Answer 1

Given :    (7a+b–c+d)²+(d-b-5a+c)²+2(7a+d+b-c)(c+d-b-5a)  

To find : To be expressed as perfect Square

Solution:

(7a+b–c+d)²+(d-b-5a+c)²+2(7a+d+b-c)(c+d-b-5a)

Lets change order of some

(7a + d + b - c)²  + (c + d - b - 5a)² + 2(7a+d+b-c)(c+d-b-5a)

now using

x² + y ²  + 2xy  = (x + y)²

x = 7a + d + b - c

y = c + d - b - 5a

= ( 7a + d + b - c  + c + d - b - 5a)²

= ( 2a + 2d )²

= (2(a + d))²

(7a+b–c+d)²+(d-b-5a+c)²+2(7a+d+b-c)(c+d-b-5a)  = (2(a + d))²

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