Factoring Differences of Squares

Match  $121-x^2$ with it's factored form. 

•  $\left(x-11\right)\left(x+11\right)$  

•  $\left(x+10\right)\left(x-10\right)$  

•  $\left(11-x\right)\left(11+x\right)$  

•  $\left(11-x\right)\left(11-x\right)$  

Change the factored form expression into standard form.

 $\left(y+x\right)\left(y-x\right)$  

•  $y^2-2xy-x^2$  

•  $x^2-2xy+y^2$  

•  $x^2-y^2$  

•  $y^2-x^2$  

Change the factored form expression into standard form.

 $\left(x-y\right)\left(x-y\right)$  

•  $x^2-y^2$  

•  $x^2-2xy+y^2$  

•  $x^2+2xy+y^2$  

•  $x^2+2xy-y^2$  

Are

 $\left(x+3\right)\left(x-3\right)$  and  $\left(3+x\right)\left(3-x\right)$  equivalent when you change each factored form expression to standard form?

• Yes!  Both factored forms contain a sum and difference of 3 and x.

• No!  While both factored forms contain a sum and difference of 3 and x,  the first is  $x^2-9$  and the 2nd is  $9-x^2$  .

Write $x^2-144$  in factored form.

•  $\left(x+12\right)\left(x+12\right)$  

•  $\left(x+12\right)\left(x-12\right)$  

•  $\left(x-12\right)\left(x-12\right)$  

Change $x^2-25$  into factored form.

•  $\left(x+25\right)\left(x-25\right)$  

•  $\left(x+5\right)\left(x+5\right)$  

• Not possible.

•  $\left(x+5\right)\left(x-5\right)$  

Change $a^2-b^2$  into factored form.

•  $\left(a+b\right)\left(a-b\right)$  

•  $\left(a+b\right)\left(a+b\right)$  

•  $\left(a-b\right)\left(a-b\right)$  

• Not Possible.

Change $100+y^2$  into factored form.

•  $\left(10+y\right)\left(10-y\right)$  

•  $\left(10+y\right)\left(10+y\right)$  

•  $\left(10-y\right)\left(10-y\right)$  

• Not Possible.

What are the solutions to $\left(x-4\right)\left(x+3\right)=0$  ?

Check all that apply.

• 3

• 4

• -4

• -3

Change $x^2-10x+21$  to factored form.  Check the box for each factor.

•  $\left(x-7\right)$  

•  $\left(x+7\right)$  

•  $\left(x-3\right)$  

•  $\left(x+3\right)$