Difference of Perfect Squares Factoring

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? 

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: $$x^2+26x+169$$

.

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

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

• $$\left(x+13\right)^2$$  

• $$\left(x+17\right)^2$$