How do you do factoring equations?

Question

I forgot how to do 4m^2-1=0. The teacher did not give us an example for that one. Thank you.

Answer 1

To solve for m, you can:

4m² - 1 = 0

4m² = 1

m² = 1/4

m = √(1/4)

m = 1/2 or -1/2

--OR--

Using the difference of 2 squares, i.e. x² - y² = (x - y)(x + y):

x = 2m and y = 1

(2m + 1)(2m - 1)

m = 1/2 or m = -1/2

Answer 2

This equation is the difference of two squares.  

Remember that a^2 - b^2  factors to (a+b)(a-b)

In this equation:  4m^2 - 1 = 0

think...a^2 is replaced by 4m^2, and b^2 is replaced by 1

So, 4m^2 - 1 = 0 is the same as

(2m + 1)(2m -1) = 0

Answer 3

4m^2-1 =

Notice that this is the difference between 2 squares.

4m^2-1 = (2m)^2 - (1)^2

We know that:

a^2 - b^2 = (a - b)(a + b)

Given: 4m^2-1 = (2m)^2 - (1)^2

Means: a = 2m, b = 1

Just plug it into the formula.

4m^2-1 = (2m)^2 - (1)^2 = (2m - 1)(2m + 1)

Answer 4

add 1 to both sides       4m^2=1

divide by 4                   m^2=1/4

square root                  m= (+-) 1/2

Answer 5

x^2 - y^2 = (x+y)(x-y)

(2m)^2 - 1^2 = (2m + 1)(2m-1)