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

Factor y^2+4*y+3 squared

An expression to simplify:

The solution

You have entered [src] 
 2          
y  + 4*y + 3
$$\left(y^{2} + 4 y\right) + 3$$ 
y^2 + 4*y + 3
Factorization [src] 
(x + 3)*(x + 1)
$$\left(x + 1\right) \left(x + 3\right)$$ 
(x + 3)*(x + 1)
General simplification [src] 
     2      
3 + y  + 4*y
$$y^{2} + 4 y + 3$$ 
3 + y^2 + 4*y
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(y^{2} + 4 y\right) + 3$$
To do this, let's use the formula
$$a y^{2} + b y + c = a \left(m + y\right)^{2} + n$$
where
$$m = \frac{b}{2 a}$$
$$n = \frac{4 a c - b^{2}}{4 a}$$
In this case
$$a = 1$$
$$b = 4$$
$$c = 3$$
Then
$$m = 2$$
$$n = -1$$
So,
$$\left(y + 2\right)^{2} - 1$$
Numerical answer [src] 
3.0 + y^2 + 4.0*y
3.0 + y^2 + 4.0*y
Trigonometric part [src] 
     2      
3 + y  + 4*y
$$y^{2} + 4 y + 3$$ 
3 + y^2 + 4*y
Assemble expression [src] 
     2      
3 + y  + 4*y
$$y^{2} + 4 y + 3$$ 
3 + y^2 + 4*y
Rational denominator [src] 
     2      
3 + y  + 4*y
$$y^{2} + 4 y + 3$$ 
3 + y^2 + 4*y
Common denominator [src] 
     2      
3 + y  + 4*y
$$y^{2} + 4 y + 3$$ 
3 + y^2 + 4*y
Combining rational expressions [src] 
3 + y*(4 + y)
$$y \left(y + 4\right) + 3$$ 
3 + y*(4 + y)
Combinatorics [src] 
(1 + y)*(3 + y)
$$\left(y + 1\right) \left(y + 3\right)$$ 
(1 + y)*(3 + y)
Powers [src] 
     2      
3 + y  + 4*y
$$y^{2} + 4 y + 3$$ 
3 + y^2 + 4*y
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