Mister Exam

Other calculators

Expression simplification/ Factor perfect squares/ -y^2+y+3

Factor -y^2+y+3 squared

An expression to simplify:

The solution

You have entered [src] 
   2        
- y  + y + 3
(−y2+y)+3\left(- y^{2} + y\right) + 3 
-y^2 + y + 3
General simplification [src] 
         2
3 + y - y
−y2+y+3- y^{2} + y + 3 
3 + y - y^2
The perfect square
Let's highlight the perfect square of the square three-member
(−y2+y)+3\left(- y^{2} + y\right) + 3
To do this, let's use the formula
ay2+by+c=a(m+y)2+na y^{2} + b y + c = a \left(m + y\right)^{2} + n
where
m=b2am = \frac{b}{2 a}
n=4ac−b24an = \frac{4 a c - b^{2}}{4 a}
In this case
a=−1a = -1
b=1b = 1
c=3c = 3
Then
m=−12m = - \frac{1}{2}
n=134n = \frac{13}{4}
So,
134−(y−12)2\frac{13}{4} - \left(y - \frac{1}{2}\right)^{2}
Factorization [src] 
/            ____\ /            ____\
|      1   \/ 13 | |      1   \/ 13 |
|x + - - + ------|*|x + - - - ------|
\      2     2   / \      2     2   /
(x+(−12+132))(x+(−132−12))\left(x + \left(- \frac{1}{2} + \frac{\sqrt{13}}{2}\right)\right) \left(x + \left(- \frac{\sqrt{13}}{2} - \frac{1}{2}\right)\right) 
(x - 1/2 + sqrt(13)/2)*(x - 1/2 - sqrt(13)/2)
Numerical answer [src] 
3.0 + y - y^2
3.0 + y - y^2
Assemble expression [src] 
         2
3 + y - y
−y2+y+3- y^{2} + y + 3 
3 + y - y^2
Combinatorics [src] 
         2
3 + y - y
−y2+y+3- y^{2} + y + 3 
3 + y - y^2
Common denominator [src] 
         2
3 + y - y
−y2+y+3- y^{2} + y + 3 
3 + y - y^2
Powers [src] 
         2
3 + y - y
−y2+y+3- y^{2} + y + 3 
3 + y - y^2
Combining rational expressions [src] 
3 + y*(1 - y)
y(1−y)+3y \left(1 - y\right) + 3 
3 + y*(1 - y)
Trigonometric part [src] 
         2
3 + y - y
−y2+y+3- y^{2} + y + 3 
3 + y - y^2
Rational denominator [src] 
         2
3 + y - y
−y2+y+3- y^{2} + y + 3 
3 + y - y^2
    © Mister Exam – Calculator