D.O.T.S.

Difference of Two Squares (D.O.T.S.)

- A difference of two squares (D.O.T.S.) occurs when you are multiplying two binomials that are the same but with different signs.

- For Example:

the same but different signs!

the same but different signs!

Multiple Select

Which of the following is a difference of two squares (D.O.T.S.)?

Select all that apply

• $$\left(2x+3\right)\left(2x+3\right)$$

• $$\left(2x-9\right)\left(2x+9\right)$$

• $$\left(3x-2\right)\left(3x-2\right)$$

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

• $$\left(x-2\right)\left(x+3\right)$$

Multiple Select

Which of the following is a difference of two squares (D.O.T.S.)?

Select all that apply

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

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

• $$\left(5x-2\right)\left(5x-2\right)$$

• $$\left(x+1\right)\left(x+1\right)$$

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

Dropdown

(x + 3)(x - 3) ​

Select answer

a difference of two squares (D.O.T.S.).

Dropdown

(x - 3)(x + 3) ​

Select answer

a difference of two squares (D.O.T.S.).

Dropdown

(x - 3)(x - 3) ​

Select answer

a difference of two squares (D.O.T.S.).

Dropdown

(5x - 3)(5x - 3) ​

Select answer

a difference of two squares (D.O.T.S.).

Dropdown

(5x - 3)(5x + 3) ​

Select answer

a difference of two squares (D.O.T.S.).

Difference of Two Squares (D.O.T.S.)

- When multipying a difference of two squares, the middle terms will always cancel out.

- For Example:

the "-5x" and "+5x" cancelled each other out!

the "+14x" and "-14x" cancelled each other out!

Difference of Two Squares (D.O.T.S.)

- Therefore, when multiplying this type, we can use the shortcut below!

- Examples:

Multiple Choice

Multiply: $$\left(x+6\right)\left(x-6\right)$$

• $$x^2+36$$

• $$x^2-36$$

• $$2x^2-6$$

• $$x^2-6$$

Multiple Choice

Multiply: $$\left(x-1\right)\left(x+1\right)$$

• $$x^2+1$$

• $$x^2-2$$

• $$2x^2-1$$

• $$x^2-1$$

Multiple Choice

Multiply: $$\left(3x+1\right)\left(3x-1\right)$$

• $$9x^2-1$$

• $$3x^2-1$$

• $$3x^2+1$$

• $$9x^2-2$$

Multiple Choice

Multiply: $$\left(2x+5\right)\left(2x-5\right)$$

• $$4x^2+25$$

• $$4x^2-5$$

• $$4x^2-25$$

• $$2x^2-25$$

Match

Match the following:

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

• $$\left(2x+1\right)\left(2x-1\right)$$

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

• $$\left(4x-1\right)\left(4x+1\right)$$

• $$\left(4x+2\right)\left(4x-2\right)$$

• $$x^2-4$$

• $$4x^2-1$$

• $$x^2-16$$

• $$16x^2-1$$

• $$16x^2-4$$

Math Response

Multiply: $$\left(x+5\right)\left(x-5\right)$$

Type answer here

Correct Answer: x^2-25

Deg^°

Rad

Math Response

Multiply: $$\left(x-7\right)\left(x+7\right)$$

Type answer here

Correct Answer: x^2-49

Deg^°

Rad

Math Response

Multiply: $$\left(3x+5\right)\left(3x-5\right)$$

Type answer here

Correct Answer: 9x^2-25

Deg^°

Rad

Math Response

Multiply: $$\left(5x-7\right)\left(5x+7\right)$$

Type answer here

Correct Answer: 25x^2-49

Deg^°

Rad

Math Response

Multiply: $$\left(7x-1\right)\left(7x+1\right)$$

Type answer here

Correct Answer: 49x^2-1

Deg^°

Rad