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Expression simplification/ Factor perfect squares/ x^2+8*x+15

Factor x^2+8*x+15 squared

An expression to simplify:

The solution

You have entered [src] 
 2           
x  + 8*x + 15
$$\left(x^{2} + 8 x\right) + 15$$ 
x^2 + 8*x + 15
Factorization [src] 
(x + 5)*(x + 3)
$$\left(x + 3\right) \left(x + 5\right)$$ 
(x + 5)*(x + 3)
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(x^{2} + 8 x\right) + 15$$
To do this, let's use the formula
$$a x^{2} + b x + c = a \left(m + x\right)^{2} + n$$
where
$$m = \frac{b}{2 a}$$
$$n = \frac{4 a c - b^{2}}{4 a}$$
In this case
$$a = 1$$
$$b = 8$$
$$c = 15$$
Then
$$m = 4$$
$$n = -1$$
So,
$$\left(x + 4\right)^{2} - 1$$
General simplification [src] 
      2      
15 + x  + 8*x
$$x^{2} + 8 x + 15$$ 
15 + x^2 + 8*x
Numerical answer [src] 
15.0 + x^2 + 8.0*x
15.0 + x^2 + 8.0*x
Assemble expression [src] 
      2      
15 + x  + 8*x
$$x^{2} + 8 x + 15$$ 
15 + x^2 + 8*x
Combining rational expressions [src] 
15 + x*(8 + x)
$$x \left(x + 8\right) + 15$$ 
15 + x*(8 + x)
Trigonometric part [src] 
      2      
15 + x  + 8*x
$$x^{2} + 8 x + 15$$ 
15 + x^2 + 8*x
Rational denominator [src] 
      2      
15 + x  + 8*x
$$x^{2} + 8 x + 15$$ 
15 + x^2 + 8*x
Common denominator [src] 
      2      
15 + x  + 8*x
$$x^{2} + 8 x + 15$$ 
15 + x^2 + 8*x
Powers [src] 
      2      
15 + x  + 8*x
$$x^{2} + 8 x + 15$$ 
15 + x^2 + 8*x
Combinatorics [src] 
(3 + x)*(5 + x)
$$\left(x + 3\right) \left(x + 5\right)$$ 
(3 + x)*(5 + x)
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