Answer:
Step-by-step explanation:
To factor the equation 9^x - 3^x - 56 = 0, let's make a substitution. Let's substitute y = 3^x.
By substituting y = 3^x, we can rewrite the equation as follows:
y^2 - y - 56 = 0
Now we can factor this quadratic equation. We need to find two numbers that multiply to -56 and add up to -1. After some trial and error, we find that the numbers are -8 and 7. So we can rewrite the equation as:
(y - 8)(y + 7) = 0
Now let's substitute back y = 3^x:
(3^x - 8)(3^x + 7) = 0
So, the factored form of the equation 9^x - 3^x - 56 = 0 is (3^x - 8)(3^x + 7) = 0.
