Mister Exam

Other calculators

Expression simplification/ Factor perfect squares/ y^2+4*y*x+3*x^2

Factor y^2+4*y*x+3*x^2 squared

An expression to simplify:

The solution

You have entered [src] 
 2              2
y  + 4*y*x + 3*x
$$3 x^{2} + \left(x 4 y + y^{2}\right)$$ 
y^2 + (4*y)*x + 3*x^2
General simplification [src] 
 2      2        
y  + 3*x  + 4*x*y
$$3 x^{2} + 4 x y + y^{2}$$ 
y^2 + 3*x^2 + 4*x*y
Factorization [src] 
        /    y\
(x + y)*|x + -|
        \    3/
$$\left(x + \frac{y}{3}\right) \left(x + y\right)$$ 
(x + y)*(x + y/3)
The perfect square
Let's highlight the perfect square of the square three-member
$$3 x^{2} + \left(x 4 y + y^{2}\right)$$
Let us write down the identical expression
$$3 x^{2} + \left(x 4 y + y^{2}\right) = - \frac{y^{2}}{3} + \left(3 x^{2} + 4 x y + \frac{4 y^{2}}{3}\right)$$
or
$$3 x^{2} + \left(x 4 y + y^{2}\right) = - \frac{y^{2}}{3} + \left(\sqrt{3} x + \frac{2 \sqrt{3} y}{3}\right)^{2}$$
in the view of the product
$$\left(- \frac{y}{\sqrt{3}} + \left(\sqrt{3} x + \frac{2 \sqrt{3}}{3} y\right)\right) \left(\frac{y}{\sqrt{3}} + \left(\sqrt{3} x + \frac{2 \sqrt{3}}{3} y\right)\right)$$
$$\left(- \frac{\sqrt{3}}{3} y + \left(\sqrt{3} x + \frac{2 \sqrt{3}}{3} y\right)\right) \left(\frac{\sqrt{3}}{3} y + \left(\sqrt{3} x + \frac{2 \sqrt{3}}{3} y\right)\right)$$
$$\left(\sqrt{3} x + y \left(- \frac{\sqrt{3}}{3} + \frac{2 \sqrt{3}}{3}\right)\right) \left(\sqrt{3} x + y \left(\frac{\sqrt{3}}{3} + \frac{2 \sqrt{3}}{3}\right)\right)$$
$$\left(\sqrt{3} x + \frac{\sqrt{3} y}{3}\right) \left(\sqrt{3} x + \sqrt{3} y\right)$$
Numerical answer [src] 
y^2 + 3.0*x^2 + 4.0*x*y
y^2 + 3.0*x^2 + 4.0*x*y
Trigonometric part [src] 
 2      2        
y  + 3*x  + 4*x*y
$$3 x^{2} + 4 x y + y^{2}$$ 
y^2 + 3*x^2 + 4*x*y
Assemble expression [src] 
 2      2        
y  + 3*x  + 4*x*y
$$3 x^{2} + 4 x y + y^{2}$$ 
y^2 + 3*x^2 + 4*x*y
Combining rational expressions [src] 
   2              
3*x  + y*(y + 4*x)
$$3 x^{2} + y \left(4 x + y\right)$$ 
3*x^2 + y*(y + 4*x)
Common denominator [src] 
 2      2        
y  + 3*x  + 4*x*y
$$3 x^{2} + 4 x y + y^{2}$$ 
y^2 + 3*x^2 + 4*x*y
Combinatorics [src] 
(x + y)*(y + 3*x)
$$\left(x + y\right) \left(3 x + y\right)$$ 
(x + y)*(y + 3*x)
Rational denominator [src] 
 2      2        
y  + 3*x  + 4*x*y
$$3 x^{2} + 4 x y + y^{2}$$ 
y^2 + 3*x^2 + 4*x*y
Powers [src] 
 2      2        
y  + 3*x  + 4*x*y
$$3 x^{2} + 4 x y + y^{2}$$ 
y^2 + 3*x^2 + 4*x*y
    © Mister Exam – Calculator