Difference of Two Squares & Perfect Squares

Difference of Two Squares & Perfect Square Trinomials

Difference of Two Squares

 $a^2-b^2=\left(a+b\right)\left(a-b\right)$  

Multiple Choice

Factor the following expression:

 $x^2-81$  

• (x-9)(x-9)

• (x+9)(x+9)

• (x+9)(x-9)

• Not Factorable

Multiple Choice

Factor the following expression:

 $x^2-144$  

• (x-12)(x+12)

• (x-12)(x-12)

• (x+12)(x+12)

• Not Factorable

Multiple Choice

Factor the following expression:

 $x^2+64$  

• (x+8)(x+8)

• (x-8)(x-8)

• (x-8)(x+8)

• Not Factorable

Multiple Choice

Multiply the following factors:  $\left(x+2\right)\left(x-2\right)$  

•  $x^2+4x+4$ 

•  $x^2-4x+4$  
  

•  $x^{2\ }-4x-4$  
  

•  $x^2-4$  
  

•  $x^2+4x-4$  

Multiple Choice

Multiply the following factors:  $\left(x-3\right)\left(x+3\right)$  

•  $x^2+9x+9$ 

•  $x^2-9$  
  

•  $x^{2\ }-9x-9$  
  

•  $x^2-9x+9$  
  

•  $x^2+9x-9$  

Multiple Choice

Multiply the following factors:  $\left(x-10\right)\left(x+10\right)$  

•  $x^2-100$ 

•  $x^2-50x+100$  
  

•  $x^{2\ }-x-100$  
  

•  $x^2-20x+20$  
  

•  $x^2+x-10$  

Multiple Select

Check all the expressions that are difference of two squares.

• $x^2-25$

• $x^2-100$

• $x^2+36$

• $x^2-73$

• $16x^2-400$

Open Ended

Why is

 $x^2+36$ not difference of two squares? 

Open Ended

Why is

 $x^2-73$ not difference of two squares? 

Fill in the Blank

Factor

 $x^2-121$  

Poll

Is

 $x^2+49$  factorable, by difference of two squares?

• Yes

• No

Perfect Square Trinomials

What is a Perfect Square Trinomial?

Multiple Choice

Can the expression $\left(x+2\right)\left(x+2\right)$ 

also be written as  $\left(x+2\right)^2$ ?

• Yes

• No

Multiple Choice

Expand the following expression: $\left(x+2\right)^2$ 

.

•  $x^2+4x+4$  

•  $x^2-4x+4$  

•  $x^2-4$  

•  $x^2+4$  

Multiple Choice

Expand the following expression: $\left(x-2\right)^2$ 

.

•  $x^2+4x+4$  

•  $x^2-4x+4$  

•  $x^2-4$  

•  $x^2+4$  

Multiple Choice

Expand the following expression: $\left(x+6\right)^2$ 

.

•  $x^2+12x+36$  

•  $x^2-12x+36$  

•  $x^2-36$  

•  $x^2+36$  

Multiple Choice

Expand the following expression: $\left(x-6\right)^2$ 

.

•  $x^2+12x+36$  

•  $x^2-12x+36$  

•  $x^2-36$  

•  $x^2+36$  

Multiple Select

Select all that are factors of  the following expression: $x^2+16x+64$ 

.

•  $\left(x+4\right)\left(x+4\right)$  

•  $\left(x+8\right)^2$  

•  $\left(x+8\right)\left(x+8\right)$  

•  $\left(x+16\right)^2$  

Multiple Select

Select all that are factors of  the following expression: $x^2-20x+100$ 

.

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

•  $\left(x+5\right)\left(x-20\right)$  

•  $\left(x+20\right)\left(x-5\right)$  

•  $\left(x-10\right)^2$  

Multiple Select

Select all that are factors of  the following expression: $x^2-6x+9$ 

.

•  $\left(x-4.5\right)\left(x-2\right)$  

•  $\left(x-3\right)\left(x-3\right)$  

•  $\left(x-9\right)\left(x-1\right)$  

•  $\left(x-3\right)^2$  

Multiple Select

Select all that are factors of  the following expression: $x^2+10x+25$ 

.

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

•  $\left(x+10\right)\left(x+15\right)$  

•  $\left(x+5\right)^2$  

•  $\left(x-5\right)^2$  

Multiple Select

Select all that are factors of  the following expression: $x^2+26x+169$ 

.

•  $\left(x+17\right)\left(x+17\right)$  

•  $\left(x+13\right)\left(x+13\right)$  

•  $\left(x+13\right)^2$  

•  $\left(x+17\right)^2$