Mister Exam

# Factor polynomial a^2+8*a+16

An expression to simplify:

### The solution

You have entered [src]
 2
a  + 8*a + 16
$$\left(a^{2} + 8 a\right) + 16$$
a^2 + 8*a + 16
Factorization [src]
a + 4
$$a + 4$$
a + 4
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(a^{2} + 8 a\right) + 16$$
To do this, let's use the formula
$$a^{3} + a b + c = a \left(a + m\right)^{2} + n$$
where
$$m = \frac{b}{2 a}$$
$$n = \frac{4 a c - b^{2}}{4 a}$$
In this case
$$a = 1$$
$$b = 8$$
$$c = 16$$
Then
$$m = 4$$
$$n = 0$$
So,
$$25$$
General simplification [src]
      2
16 + a  + 8*a
$$a^{2} + 8 a + 16$$
16 + a^2 + 8*a
16.0 + a^2 + 8.0*a
16.0 + a^2 + 8.0*a
Assemble expression [src]
      2
16 + a  + 8*a
$$a^{2} + 8 a + 16$$
16 + a^2 + 8*a
Powers [src]
      2
16 + a  + 8*a
$$a^{2} + 8 a + 16$$
16 + a^2 + 8*a
Rational denominator [src]
      2
16 + a  + 8*a
$$a^{2} + 8 a + 16$$
16 + a^2 + 8*a
Trigonometric part [src]
      2
16 + a  + 8*a
$$a^{2} + 8 a + 16$$
16 + a^2 + 8*a
Common denominator [src]
      2
16 + a  + 8*a
$$a^{2} + 8 a + 16$$
16 + a^2 + 8*a
Combining rational expressions [src]
16 + a*(8 + a)
$$a \left(a + 8\right) + 16$$
16 + a*(8 + a)
Combinatorics [src]
       2
(4 + a) 
$$\left(a + 4\right)^{2}$$
(4 + a)^2