<span>The correct answer is 2x</span>²<span>-16x+30.
Explanation<span>: (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 2x</span></span>²<span><span>, we have 2(x-3)</span></span>²<span><span>, and instead of -4x, we have -4(x-3).
This gives us 2(x-3)</span></span>²<span><span>-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(x</span></span>²<span><span>-3x-3x+9)-(4x-12) =2(x</span></span>²<span><span>-6x+9)-4x+12.
Using the distributive property gives us 2*x</span></span>²<span><span>-2*6x+2*9-4x+12 =2x</span></span>²<span><span>-12x+19-4x+12.
Combine like terms, and we have 2x</span></span>²<span><span>-16x+30.</span></span>
