Question

How do you solve by factoring and using the principle of zero products: `64v^2=36`?

Answer 1

`v in {-3/4, 3/4}`

Explanation:

The zero product principle states that if `ab = 0` then `a=0` or `b=0`. Together with the special product `a^2-b^2 = (a+b)(a-b)`, we can solve for `v`:

`64v^2 = 36`

`=> 64v^2 - 36 = 0`

`=> (8v)^2 - 6^2 = 0`

`=> (8v+6)(8v-6) = 0`

`=> 8v+6 = 0 or 8v-6 = 0`

`=> 8v = -6 or 8v = 6`

`=> v = -6/8 or v = 6/8`

`:. v in {-3/4, 3/4}`