Write the following equations in factored form. Remember common factors first
(if possible).) π¦ = 16π₯^2 β 9
π¦ = (4π₯ β 3)(4π₯ + 3)
To write the equation π¦ = 16π₯^2 β 9 in factored form, we can first try to look for any common factors. However, in this case, there are no common factors among the terms.
So, to factorize the given equation, we can use the difference of squares formula which states that a^2 - b^2 can be factored as (a + b)(a - b).
Applying the difference of squares formula, we can rewrite the equation as:
π¦ = (4π₯)^2 - 3^2
Now, we can see that we have a difference of squares, where a = 4π₯ and b = 3. Applying the formula, we get:
π¦ = (4π₯ + 3)(4π₯ - 3)
Therefore, the equation π¦ = 16π₯^2 β 9 in factored form is π¦ = (4π₯ + 3)(4π₯ - 3).