Mister Exam

# Factor polynomial u^2+2*u*v+v^2

An expression to simplify:

### The solution

You have entered [src]
 2            2
u  + 2*u*v + v 
$$v^{2} + \left(u^{2} + 2 u v\right)$$
u^2 + (2*u)*v + v^2
The perfect square
Let's highlight the perfect square of the square three-member
$$v^{2} + \left(u^{2} + 2 u v\right)$$
Let us write down the identical expression
$$v^{2} + \left(u^{2} + 2 u v\right) = 0 v^{2} + \left(u^{2} + 2 u v + v^{2}\right)$$
or
$$v^{2} + \left(u^{2} + 2 u v\right) = 0 v^{2} + \left(u + v\right)^{2}$$
Factorization [src]
u + v
$$u + v$$
u + v
General simplification [src]
 2    2
u  + v  + 2*u*v
$$u^{2} + 2 u v + v^{2}$$
u^2 + v^2 + 2*u*v
Combinatorics [src]
       2
(u + v) 
$$\left(u + v\right)^{2}$$
(u + v)^2
Powers [src]
 2    2
u  + v  + 2*u*v
$$u^{2} + 2 u v + v^{2}$$
u^2 + v^2 + 2*u*v
Trigonometric part [src]
 2    2
u  + v  + 2*u*v
$$u^{2} + 2 u v + v^{2}$$
u^2 + v^2 + 2*u*v
Common denominator [src]
 2    2
u  + v  + 2*u*v
$$u^{2} + 2 u v + v^{2}$$
u^2 + v^2 + 2*u*v
Combining rational expressions [src]
 2
v  + u*(u + 2*v)
$$u \left(u + 2 v\right) + v^{2}$$
v^2 + u*(u + 2*v)
Rational denominator [src]
 2    2
u  + v  + 2*u*v
$$u^{2} + 2 u v + v^{2}$$
u^2 + v^2 + 2*u*v
u^2 + v^2 + 2.0*u*v
u^2 + v^2 + 2.0*u*v
 2    2
u  + v  + 2*u*v
$$u^{2} + 2 u v + v^{2}$$
u^2 + v^2 + 2*u*v