Question

.சுருக்குக


"(ii) " (x^3-y^3)/(3x^2+9x+6y^2 )×(x^2+2xy+y^2)/(x^2-y^2 )

Answer 1

சுருக்குக $\frac{x^{3}-y^{3}}{3 x^{2}+9 x y+6 y^{2}} \times \frac{x^{2}+2 x y+y^{2}}{x^{2}-y^{2}}$  

தீர்வு:    

கொடுக்கப்பட்டது   = $\frac{x^{3}-y^{3}}{3 x^{2}+9 x y+6 y^{2}} \times \frac{x^{2}+2 x y+y^{2}}{x^{2}-y^{2}}$

= $\frac{(x-y)\left(x^{2}+x y+y^{2}\right)}{3 x^{2}+6 x y+3 x y+6 y^{2}} \times \frac{(x+y)^{2}}{(x+y)(x-y)}$

= $\frac{\left(x^{2}+x y+y^{2}\right)(x+y)}{3 x(x+2 y)+3 y(x+2 y)}$  

= $\frac{(x+y)\left(x^{2}+x y+y^{2}\right)}{(3 x+3 y)(x+2 y)}$

= $\frac{(x+y)\left(x^{2}+x y+y^{2}\right)}{3(x+y)(x+2 y)}$  

⇒$\frac{\left(x^{2}+x y+y^{2}\right)}{3(x+2 y)}$

விடை: $\frac{\left(x^{2}+x y+y^{2}\right)}{3(x+2 y)}$