Question

How do you simplify $3x\left( x-1 \right)-4\left( {{x}^{2}}-x \right)$?

Answer 1

Hint: First multiply ‘x’ with $\left( x-1 \right)$ to get $\left( {{x}^{2}}-x \right)$ in both the terms. Then take $\left( {{x}^{2}}-x \right)$ common from both the terms. Multiply $-1$ separately with each term of $\left( {{x}^{2}}-x \right)$. Again take out common as ‘x’ from the previous result to get the required solution.

Complete step by step solution:
Considering our question $3x\left( x-1 \right)-4\left( {{x}^{2}}-x \right)$
Multiplying ‘x’ with $\left( x-1 \right)$, we get
$\Rightarrow 3\left( {{x}^{2}}-x \right)-4\left( {{x}^{2}}-x \right)$
Since, we have $\left( {{x}^{2}}-x \right)$ in both the terms now, so taking common $\left( {{x}^{2}}-x \right)$, we get
$\begin{align}
  & \Rightarrow \left( {{x}^{2}}-x \right)\left( 3-4 \right) \\
 & \Rightarrow \left( {{x}^{2}}-x \right)\left( -1 \right) \\
\end{align}$
Multiplying $-1$ with each term separately, we get
$\Rightarrow x-{{x}^{2}}$
Again, taking common out ‘x’ from both the terms, we get
$\Rightarrow x\left( 1-x \right)$
So, $3x\left( x-1 \right)-4\left( {{x}^{2}}-x \right)$ can be simplified as $x\left( 1-x \right)$.
This is the required solution of the given question.

Note: Multiplying ‘x’ with $\left( x-1 \right)$ should be the first approach for solving this question. So, we get $\left( {{x}^{2}}-x \right)$ in both the terms which can be taken out for further simplification. We obtained $x-{{x}^{2}}$, which could be the solution, but the solution should be in maximum simplified form. So, taking out the common ‘x’ from both the terms we get $x\left( 1-x \right)$ as the solution, which is in maximum factored form. Hence, it is the appropriate solution to the given question.