Mister Exam

Other calculators

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

Factor x^2+x*b+4*b^2 squared

An expression to simplify:

The solution

You have entered [src] 
 2            2
x  + x*b + 4*b
$$4 b^{2} + \left(b x + x^{2}\right)$$ 
x^2 + x*b + 4*b^2
The perfect square
Let's highlight the perfect square of the square three-member
$$4 b^{2} + \left(b x + x^{2}\right)$$
Let us write down the identical expression
$$4 b^{2} + \left(b x + x^{2}\right) = \frac{15 x^{2}}{16} + \left(4 b^{2} + b x + \frac{x^{2}}{16}\right)$$
or
$$4 b^{2} + \left(b x + x^{2}\right) = \frac{15 x^{2}}{16} + \left(2 b + \frac{x}{4}\right)^{2}$$
Factorization [src] 
/      /         ____\\ /      /        ____\\
|    x*\-1 + I*\/ 15 /| |    x*\1 + I*\/ 15 /|
|b - -----------------|*|b + ----------------|
\            8        / \           8        /
$$\left(b - \frac{x \left(-1 + \sqrt{15} i\right)}{8}\right) \left(b + \frac{x \left(1 + \sqrt{15} i\right)}{8}\right)$$ 
(b - x*(-1 + i*sqrt(15))/8)*(b + x*(1 + i*sqrt(15))/8)
General simplification [src] 
 2      2      
x  + 4*b  + b*x
$$4 b^{2} + b x + x^{2}$$ 
x^2 + 4*b^2 + b*x
Rational denominator [src] 
 2      2      
x  + 4*b  + b*x
$$4 b^{2} + b x + x^{2}$$ 
x^2 + 4*b^2 + b*x
Numerical answer [src] 
x^2 + 4.0*b^2 + b*x
x^2 + 4.0*b^2 + b*x
Common denominator [src] 
 2      2      
x  + 4*b  + b*x
$$4 b^{2} + b x + x^{2}$$ 
x^2 + 4*b^2 + b*x
Powers [src] 
 2      2      
x  + 4*b  + b*x
$$4 b^{2} + b x + x^{2}$$ 
x^2 + 4*b^2 + b*x
Assemble expression [src] 
 2      2      
x  + 4*b  + b*x
$$4 b^{2} + b x + x^{2}$$ 
x^2 + 4*b^2 + b*x
Combinatorics [src] 
 2      2      
x  + 4*b  + b*x
$$4 b^{2} + b x + x^{2}$$ 
x^2 + 4*b^2 + b*x
Trigonometric part [src] 
 2      2      
x  + 4*b  + b*x
$$4 b^{2} + b x + x^{2}$$ 
x^2 + 4*b^2 + b*x
Combining rational expressions [src] 
   2            
4*b  + x*(b + x)
$$4 b^{2} + x \left(b + x\right)$$ 
4*b^2 + x*(b + x)
    © Mister Exam – Calculator