Write the following equations in factored form. Remember to common factor first
(if possible)
𝑦 = 16𝑥^2 − 9
𝑦 = (4𝑥 − 3)(4𝑥 + 3)
To write the equation 𝑦 = 16𝑥^2 − 9 in factored form, we need to factor the expression 16𝑥^2 − 9.
First, we observe that the expression 16𝑥^2 − 9 is a difference of squares because it can be rewritten as (4𝑥)^2 - 3^2.
Using the formula a^2 - b^2 = (a + b)(a - b), we can factor the expression as follows:
𝑦 = (4𝑥 + 3)(4𝑥 - 3)
Therefore, the factored form of the equation 𝑦 = 16𝑥^2 − 9 is 𝑦 = (4𝑥 + 3)(4𝑥 - 3).