The correct answer is 2x²-16x+30.
Explanation:
(p*q)(x) is a composition of the two functions p(x) and q(x); it is the same as p(q(x)). We replace every x in p(x) with our value of q(x), x-3:
instead of 2x², we have 2(x-3)², and instead of -4x, we have -4(x-3).
This gives us 2(x-3)²-4(x-3). This is the same as 2(x-3)(x-3)-4(x-3).
Multiplying, we have
2(x*x-3*x-3*x-3(-3))-(4*x-4*3)
=2(x²-3x-3x+9)-(4x-12)
=2(x²-6x+9)-4x+12.
Using the distributive property gives us
2*x²-2*6x+2*9-4x+12
=2x²-12x+19-4x+12.
Combine like terms, and we have 2x²-16x+30.
