Question : The simplified form of $(7 x+4 y)^2+(7 x-4 y)^2$ is:
Option 1: $98 x^2+32 y^2$
Option 2: $98 x^2+32 y^2-5 x y$
Option 3: $32 x^2+98 y^2$
Option 4: $98 x^2-32 y^2$
Correct Answer: $98 x^2+32 y^2$
Solution : $(7x + 4y)^2 = 49x^2 + 16y^2+ 2 × 7x × 4y = 49x^2 + 16y^2 + 56xy$ $(7x - 4y)^2 = 49x^2 + 16y^2 - 2 × 7x × 4y = 49x^2 +16y^2 - 56xy$ So, $(7x + 4y)^2 + ( 7x - 4y)^2$ $ = 49x^2 + 16y^2 + 56xy + 49x^2 + 16y^2 - 56xy$ $= 98x^2 + 32y^2$ Hence, the correct answer is $98x^2 + 32y^2$.
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