Question

Solve: $\left( 2xy-xy \right)\left( 3xy-5 \right)$.

Answer 1

Hint: We will first start by using the distributive law to expand the given expression. Then we will collect the similar terms to perform addition or subtraction on them and solve the expression.

Complete step-by-step answer:
Now, we have to solve $\left( 2xy-xy \right)\left( 3xy-5 \right)$.
Now, we will first use the distributive law to simplify it. We know that,
$\begin{align}
  & \left( a-b \right)\left( c-d \right)=a\left( c-d \right)-b\left( c-d \right) \\
 & \Rightarrow \left( 2xy-xy \right)\left( 3xy-5 \right)=2xy\left( 3xy-5 \right)-xy\left( 3xy-5 \right) \\
 & =6{{x}^{2}}{{y}^{2}}-10xy-3{{x}^{2}}{{y}^{2}}+5xy \\
\end{align}$
Now, we will collect the terms with ${{x}^{2}}{{y}^{2}}$ and with $xy$ to further solve the expression.
$\begin{align}
  & =6{{x}^{2}}{{y}^{2}}-3{{x}^{2}}{{y}^{2}}-10xy+5xy \\
 & =3{{x}^{2}}{{y}^{2}}-5xy \\
\end{align}$
We have added the terms with coefficients like ${{x}^{2}}{{y}^{2}}\ and\ xy$. Therefore, the value of expression $\left( 2xy-xy \right)\left( 3xy-5 \right)$ on simplifying is $3{{x}^{2}}{{y}^{2}}-5xy$.

Note: It is important to note that we have used the property to solve the expression. We have used a fact that,
$\begin{align}
  & \left( a+b \right)\left( c+d \right)=a\left( c+d \right)+b\left( c+d \right) \\
 & a\left( c+d \right)=ac+ad \\
 & b\left( c+d \right)=bc+bd \\
\end{align}$