Question

Factor Completely.
25z^2 − 36w^2

Answer 1

(5z-6w)(5z+6w)

Explanation:

Hi there!

We're given the expression 25z²-36w² and we want to factor it.

The expression written as a difference of squares. The difference of squares is given as a²-b²=(a-b)(a+b)

Let's label the values of what is a² and b², and then try to determine what a and b are from that information

`a^(2)=25z^2\\b^2=36w^2`

Alright then! Let's square root both sides to find what a and b are

`√(a^2)=\sqrt{25z^2`

Which then means:

a=5z

And then for b:

`√(b^2)=√(36w^2)`

b=6w

Now substitute those values into the formula

a²-b² = (a-b)(a+b)

`25z^(2)-36w^2=(5z-6w)(5z+6w)`

Hope this helps!