Write the following equations in factored form. Remember to common factor first
(if possible) 𝑦 = 16𝑥^2 − 9
𝑦 = (4𝑥 − 3)(4𝑥 + 3)
To factor the equation 𝑦 = 16𝑥^2 − 9, we can observe that it is in the form of a difference of squares. Remember that the difference of squares pattern is given by 𝑎^2 − 𝑏^2 = (𝑎 + 𝑏)(𝑎 − 𝑏).
In this case, we have 𝑦 = 16𝑥^2 − 9, which can be rewritten as 𝑎^2 − 𝑏^2, where 𝑎 = 4𝑥 and 𝑏 = 3.
Now we can apply the difference of squares pattern:
𝑦 = (𝑎 + 𝑏)(𝑎 − 𝑏)
= (4𝑥 + 3)(4𝑥 − 3)
Therefore, the equation 𝑦 = 16𝑥^2 − 9 can be expressed in factored form as (4𝑥 + 3)(4𝑥 − 3).