Question

Simplify : (x-2/3)^2+(x+2/3)^2​

Answer 1

Answer:

$2x^{2} + (\frac{8}{9})$  

Step-by-step explanation:

$(x - (\frac{2}{3})) ^{2}$  + $(x + (\frac{2}{3})) ^{2}$

Now, by algebraic identity, we know that

        $(a+b)^{2}  = a^{2}  + b^{2}  + 2ab$

and, $(a-b)^{2}   = a^{2}  + b^{2}  - 2ab$

Applying this identity to $(x - (\frac{2}{3})) ^{2}$  , we get

$(x - (\frac{2}{3})) ^{2}$  =$x^{2}  +  (\frac{-2}{3}) ^{2}  - 2ax$

 = $x^{2}  + \frac{4}{9}  - 2ax$

Similarly, $(x+ (\frac{2}{3})) ^{2}$  = $x^{2}  + \frac{4}{9}  + 2ax$

combining both the expansions , we get

$x^{2}  + \frac{4}{9}  - 2ax$  +  $x^{2}  + \frac{4}{9}  + 2ax$

= $2x^{2} + 2(\frac{4}{9})$  = $2x^{2} + (\frac{8}{9})$