Perfect Squares

Perfect Squares

Friday Dec 11, 2020

Open Ended

Factor this difference of squares completely: 5x² - 5

Perfect Squares

Similarly to difference of squares, you can solve perfect squares using the diamond/box method or by using square roots

Solving Perfect Squares

A perfect square means the trinomial (three-term polynomial) has perfect squares (you can find the square root and have a whole number) for the leading coefficient (first number) and the constant (last number)
Once you have found the square roots, write your factor using those numbers
 $4x^2\ +\ 12x\ +\ 9$  

 $\sqrt{4}\ =\ 2,\ \ \ \ \ \ \ \sqrt{9}\ =\ 3$  
 $\left(2x\ +\ 3\right)\left(2x+3\right)\ =\ \left(2x+3\right)^2$  

Multiple Select

Select ALL  that apply

Factor the perfect square:

 $4x^2\ +\ 20x\ +\ 25$  

• (2x + 5) (2x + 5)

•  $\left(2x\ +\ 5\right)^2$  

One thing to look for...

If the middle term is a "+" --> 4x² + 12x + 9, then the factors will be "+"

(2x + 3) (2x + 3) = (2x + 3)²

If the middle term is a "-" --> 4x² - 20x + 25, then the factors will be "-"

(2x - 5) (2x - 5) = (2x - 5)²

Multiple Choice

If the middle term is a "+" what will your factors be?

• -

• +

Multiple Choice

If the middle term is a "-" what will your factors be?

• -

• +

So, what happens if you have a GCF?

 Then factor our the GCF first, and then square root the first and last terms left over and write your factors

 $3x^2\ +\ 30x\ +\ 75$    --> GCF is 3

 $3\left(x^2\ +\ 10x\ +\ 25\right)$  
 $\sqrt{1}=\ 1,\ \ \ \ \ \ \ \sqrt{25}\ =\ 5$  
 $3\ \left(x\ +\ 5\right)\ \left(x\ +\ 5\right)\ \ =\ 3\left(x\ +\ 5\right)^2$  

Multiple Choice

Factor completely:

 $100p^2\ -\ 40p\ +\ 4$  

*Remember to check for GCF first*

• Can't factor it

•  $4\left(5p\ -1\right)^2$  

• (10p - 2)(10p - 2)

If you chose (10p -2) for the last slide...

You are not wrong! However, by not factoring out the GCF first, your answer isn't in simplest terms and it will make what's next unnecessarily difficult.

Always look for a GCF first, and then square root and factor.

Practice time!

There is a worksheet in Google Classroom

Complete it however works best for you (online, or on paper and upload your work)

If you didn't do yesterday's work, make sure that is done too