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Simplify (2x − 5y)2 + (5x + 2y)2 + (2x + 5y)(2x − 5y).
Question

Simplify (2x − 5y)2 + (5x + 2y)2 + (2x + 5y)(2x − 5y).

A.

34x2 − 4y2

B.

−34x2 + 4y2

C.

−33x2 − 4y2

D.

33x2 + 4y2

Correct option is D

Given: 

(2x − 5y)2+ (5x + 2y)2+ (2x + 5y)(2x − 5y) 

Formula Used: 

(a+b)2=a2+b2+2ab (ab)2=a2+b22ab a2b2=(a+b)(ab)(a +b)^2 = a^2 +b^2+2ab \\ \ \\ (a-b)^2 = a^2 +b^2-2ab \\ \ \\ a^2 -b^2 = (a+b)(a-b)  

Solution: 

(2x − 5y)2+ (5x + 2y)2+ (2x + 5y)(2x − 5y) 

= 4x2 + 25y2 − 10xy + 25x2 + 4y2 + 10xy + 4x2 - 25y2 

=  33x2 + 4y2 


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