Question 1134048
f(x) = (x + 7) * (x - 5)^2


f(-3) = (-3 + 7) * (-3 - 5)^2
simplify to get f(-3) = 4 * (-8)^2
simplify further to get f(-3) = 4 * 64
simplify further to get f(-3) = 256


that's your solution to the first part.


for the second part, start again with f(x) = (x + 7) * (x - 5)^2


replace x with a + 3 to get:


f(a + 3) = (a + 3 + 7) * (a + 3 - 5)^2


combine like terms to get:


f(a + 3) = (a + 10) * (a - 2)^2


since (a - 2)^2 is equal to a^2 - 4a + 4, the equation becomes:


f(a + 3) = (a + 10) * (a^2 - 4a + 4)


simplify to get:


f(a + 3) = a * (a^2 - 4a + 4) + 10 * (a^2 - 4a + 4)


simplify further to get:


f(a + 3) = a^3 - 4a^2 + 4a + 10a^2 - 40a + 40


combine like terms to get:


f(a + 3) = a^3 + 6a^2 - 36a + 40


that's your final equation for f(a + 3).


to see if the final equation is equivalent to the starting equation, select a random value for a and then evaluate the starting equation and the final equation to see if they provide the same answer.


your starting equation was f(a + 3) = (a + 3 + 7) * (a + 3 - 5)^2


your final equation was f(a + 3) = a^3 + 6a^2 - 36a + 40


let a = 5.


your starting equation becomes f(5 + 3) = (5 + 3 + 7) * (5 + 3 - 5)^2
this becomes f(8) = 15 * 9 = 135


your final equation becomes f(5 + 3) = 5^3 + 6*5^2 - 36*5 + 40
this becomes f(8) = 125 + 150 - 180 + 40
this becomes f(8) = 135


starting equation and final equation provide the same answer, so the simplification must have been good.