# Factoring Expressions: (g^2 + 10g + 25)

#### jjrocks170

##### New member
We have a test tomorrow, and this is about how far I got in this expression:

(g^2+10g+25)

Can anyone help me with this expression? :?

Thanks! :mrgreen:

#### stapel

##### Super Moderator
Staff member
jjrocks170 said:
(g^2+10g+25)

Can anyone help me with this expression?
To learn how to factor quadratics (sometimes also called trinomials), please consider studying some of the many great lessons available online. :idea:

. . . . .Google results for "factoring quadratics"

. . . . .Google results for "factoring trinomials"

Once you have studied some lessons and have learned the basic terms and techniques, please attempt the exercise. If you get stuck, or if you are unsure of your steps or solution, kindly reply showing all of your work and reasoning. Thank you!

Eliz.

#### Subhotosh Khan

##### Super Moderator
Staff member
jjrocks170 said:
We have a test tomorrow, and this is about how far I got in this expression:

(g^2+10g+25)

Can anyone help me with this expression? :?

Thanks! :mrgreen:
A quadratic function

$$\displaystyle f(x) = a \cdot x^2 + b \cdot x + c$$

can be factored as:

$$\displaystyle f(x) \, = \, a \cdot x^2 + b \cdot x + c\, = a\cdot (x - x_1)\cdot (x - x_2)$$

where

$$\displaystyle x_{1} = \frac{-b \, + \, \sqrt{b^2 - 4\cdot a \cdot c}}{2\cdot a}$$

and

$$\displaystyle x_{2} = \frac{-b \, - \, \sqrt{b^2 - 4\cdot a \cdot c}}{2\cdot a}$$

However, your problem has a special form - you need not calculate this way.

recall

$$\displaystyle (a\, +\, b)^2\, = \, a^2\, +\, 2\cdot a\cdot b \, +\, b^2$$

so

$$\displaystyle g^2 \, +\, 10\cdot g \,+\, 25\, =\,g^2 \, +\, 2\cdot\,5\,\cdot g \,+\, 5^2\, =\,(g\, + \, 5)^2\, =\, (g\, + \,5)\cdot (g\, + \,5)$$