Difference of squares

 

What are difference of square?

• It is written as (a+b) (a-b)=a^2-b^2.

• The original expression is written as x^2-c.

• There is no middle term (bx), meaning it is 0x.

• There is always a negative sign, since it is difference of squares.

 

It is similar to perfect squares, since both "a" and "c" are squares of whole numbers.

However, the factors must have a product that is equal to "c", and their sum must by "b", which in this case is always zero.

 

Therefore, in order for us to get a zero, we must add and subtract the same factor. 

For example, 9x+(-9x)=0.

 

Let's try an example!

x^2-36

• Find the square root of 36.

• It is 6.

• Find the square root of 1.

• It is 1.

• So our answer is (x+6) (x-6).

• We basically write the sqaure roots of the co-efficients.

• Let's expand and check!

• (x+6) (x-6)

• x multiplied by x is x^2.

• x multiplied by (-6) is -6x.

• 6 multiplied by x is 6x.

• 6 multiplied by (-6) is -36.

• Collect like terms which are -6x+6x=0x.

• We get x^2-36.

• We are correct!

 

Remember that we must have "b" equal to 0, therefore, we must have opposite signs for the factors, such as -4 and 4.

 

Want more help?

Refer to the video on page, perfect squares!

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Try these...

1) 36x^4-49y^4

2) 16x^2-25

3) 9x^2-64

4) 49x^2-36

 

 

Answers are...

 

 

 

1) (6x^2+7y^2) (6x^2-7y^2)

2) (4x+5) (4x-5)

3) (3x+8) (3x-8)

4) (7x+6) (7x-6)