Quadratic equations of the form

\[x^2+bx+c=0\]

can be factorised to create an equation of the form

\[(x+m)(x+n)=0\text{.}\]

When we expand a factorised quadratic expression we obtain

\[(x+m)(x+n)=x^2+(m+n)x+(m \times n)\text{.}\]

To factorise an equation of the form $x^2+bx+c$, we need to find two numbers which add together to make $b$, and multiply together to make $c$.

a)

\[\simplify{x^2+{v1+v2}x+{v1*v2}=0}\]

We need to find two values that add together to make $\var{v1+v2}$ and multiply together to make $\var{v1*v2}$.

\[\begin{align}
\var{v1} \times \var{v2}&=\var{v1*v2}\\
\var{v1}+\var{v2}&=\var{v1+v2}\\
\end{align} \]

So the factorised form of the equation is

\[\simplify{(x+{v1})(x+{v2})}=0\text{.}\]

b)

We can begin factorising by finding factors of $\var{v3*v4}$ that add together to give $\var{v3+v4}$.

\[\begin{align}
\var{v3} \times \var{v4}&=\var{v3*v4}\\
\var{v3}+\var{v4}&=\var{v3+v4}\\
\end{align} \]

So the factorised form of the equation is

\[\simplify{(x+{v3})(x+{v4})}=0\text{.}\]

c)

When factorising the quadratic expression

\[\simplify{x^2+{v5*v6}=0}\]

we need to find two values that add together to make $0$ and multiply together to make $\var{v5*v6}$.

\begin{align}
\var{v5} \times \var{v6}& = \var{v5*v6}\\
\simplify[]{ {v5} + {v6}} &= 0 \\
\end{align}

So the factorised form of the equation is

\[\simplify{(x+{v5})(x+{v6})}=0\text{.}\]