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Given two quadratic expressions $f(x)$ and $g(x)$, calculate $f(x)(g(x)-f(x))$. 

Calculate the product of two quadratic expressions of the form $ax^2+bx+c$.

Calculating a quartic polynomial by squaring a quadratic expression of the form $ax^2+bx+c$.

Multiplying a linear expression of the form $mx+c$ by a quadratic expression of the form $ax^2+bx+c$. 

Finding linear combinations of two quadtratic expressions of the form $ax^2+bx+c$.

Part (a): Given two cubic functions $g(x)$ and $h(x)$ of the form $ax^3+bx^2+cx+d$, give an expression for the function $f(x)$, where $f(x)=g(x)-2h(x)$. 

Part (b): Solve $f(x)=0$.

Given two cubic functions $g(x)$ and $h(x)$ of the form $ax^3+bx^2+cx+d$, solve the equation $g(x)=2h(x)$, giving all possible solutions for $x$. 

Solving a cubic equation of the form $ax^3+bx^2+cx+d=0$.

Factorise a cubic expression into the product of three linear factors of the form $mx+c$, where one of the factors is given. 

Given a cubic expression and a linear factor, calculate the remaining quadratic factor.