Mister Exam

Other calculators

Expression simplification/ Factor perfect squares/ y^2+2*y*b+7*b^2

Factor y^2+2*y*b+7*b^2 squared

An expression to simplify:

The solution

You have entered [src] 
 2              2
y  + 2*y*b + 7*b
$$7 b^{2} + \left(b 2 y + y^{2}\right)$$ 
y^2 + (2*y)*b + 7*b^2
General simplification [src] 
 2      2        
y  + 7*b  + 2*b*y
$$7 b^{2} + 2 b y + y^{2}$$ 
y^2 + 7*b^2 + 2*b*y
The perfect square
Let's highlight the perfect square of the square three-member
$$7 b^{2} + \left(b 2 y + y^{2}\right)$$
Let us write down the identical expression
$$7 b^{2} + \left(b 2 y + y^{2}\right) = \frac{6 y^{2}}{7} + \left(7 b^{2} + 2 b y + \frac{y^{2}}{7}\right)$$
or
$$7 b^{2} + \left(b 2 y + y^{2}\right) = \frac{6 y^{2}}{7} + \left(\sqrt{7} b + \frac{\sqrt{7} y}{7}\right)^{2}$$
Factorization [src] 
/      /         ___\\ /      /        ___\\
|    y*\-1 + I*\/ 6 /| |    y*\1 + I*\/ 6 /|
|b - ----------------|*|b + ---------------|
\           7        / \           7       /
$$\left(b - \frac{y \left(-1 + \sqrt{6} i\right)}{7}\right) \left(b + \frac{y \left(1 + \sqrt{6} i\right)}{7}\right)$$ 
(b - y*(-1 + i*sqrt(6))/7)*(b + y*(1 + i*sqrt(6))/7)
Numerical answer [src] 
y^2 + 7.0*b^2 + 2.0*b*y
y^2 + 7.0*b^2 + 2.0*b*y
Trigonometric part [src] 
 2      2        
y  + 7*b  + 2*b*y
$$7 b^{2} + 2 b y + y^{2}$$ 
y^2 + 7*b^2 + 2*b*y
Common denominator [src] 
 2      2        
y  + 7*b  + 2*b*y
$$7 b^{2} + 2 b y + y^{2}$$ 
y^2 + 7*b^2 + 2*b*y
Combining rational expressions [src] 
   2              
7*b  + y*(y + 2*b)
$$7 b^{2} + y \left(2 b + y\right)$$ 
7*b^2 + y*(y + 2*b)
Rational denominator [src] 
 2      2        
y  + 7*b  + 2*b*y
$$7 b^{2} + 2 b y + y^{2}$$ 
y^2 + 7*b^2 + 2*b*y
Powers [src] 
 2      2        
y  + 7*b  + 2*b*y
$$7 b^{2} + 2 b y + y^{2}$$ 
y^2 + 7*b^2 + 2*b*y
Combinatorics [src] 
 2      2        
y  + 7*b  + 2*b*y
$$7 b^{2} + 2 b y + y^{2}$$ 
y^2 + 7*b^2 + 2*b*y
Assemble expression [src] 
 2      2        
y  + 7*b  + 2*b*y
$$7 b^{2} + 2 b y + y^{2}$$ 
y^2 + 7*b^2 + 2*b*y
    © Mister Exam – Calculator