Question

Factor Completely.
25z^2 − 36w^2

Answer 1

Answer:

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

Step-by-step 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

$\sqrt{a^2}=\sqrt{25z^2$

Which then means:

a=5z

And then for b:

$\sqrt{b^2}=\sqrt{36w^2}$

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!