Write the following equations in factored form. Remember to common factor first
(if possible)
𝑦 = 16𝑥2 − 9
𝑦 = (4𝑥 + 3)(4𝑥 − 3)
To factor the equation 𝑦 = 16𝑥^2 - 9, we can first notice that both terms have a perfect square. The first term, 16𝑥^2, is the square of 4𝑥, and the second term, -9, is the square of 3.
So, we can rewrite the equation as 𝑦 = (4𝑥)^2 - 3^2.
Now, we can use the difference of squares formula to factor the equation further. The difference of squares formula states that 𝑎^2 - 𝑏^2 can be factored as (𝑎 + 𝑏)(𝑎 - 𝑏).
Applying this formula to our equation, we have 𝑦 = (4𝑥 + 3)(4𝑥 - 3).
Therefore, the factored form of the equation 𝑦 = 16𝑥^2 - 9 is 𝑦 = (4𝑥 + 3)(4𝑥 - 3).