Question

How do you expand and simplify $f\left( x \right)=\left( x-1 \right)\left( x+3 \right)\left( x-5 \right)$ ?

Answer 1

Hint: Here we have been asked to expand and simplify the given function in $x$, we need to expand the given expression. The given function and its expression $f\left( x \right)=\left( x-1 \right)\left( x+3 \right)\left( x-5 \right)$ . For that we will perform basic arithmetic multiplication.

Complete step by step solution:
Now considering from the question we have been asked to simplify and expand an expression in the given function $f\left( x \right)=\left( x-1 \right)\left( x+3 \right)\left( x-5 \right)$ .
For doing that we will perform basic arithmetic multiplication between different expressions of the expression.
We will first multiply the expression $\left( x-1 \right)$ with $\left( x+3 \right)$ by doing this we will have $\Rightarrow f\left( x \right)=\left( {{x}^{2}}+3x-x-3 \right)\left( x-5 \right)$
By further simplifying we will have $\Rightarrow f\left( x \right)=\left( {{x}^{2}}+2x-3 \right)\left( x-5 \right)$ .
Now we will multiply $\left( x-5 \right)$ with $\left( {{x}^{2}}+2x-3 \right)$ by doing that basic operation for simplification we will have $\Rightarrow f\left( x \right)=\left( {{x}^{3}}-5{{x}^{2}}+2{{x}^{2}}-10x-3x+15 \right)$ .
Now we will further simplify this by performing basic arithmetic calculations like addition of similar terms in the expression $\Rightarrow f\left( x \right)=\left( {{x}^{3}}-3{{x}^{2}}-13x+15 \right)$.

Therefore we can conclude that the simplified and expanded operation of $f\left( x \right)=\left( x-1 \right)\left( x+3 \right)\left( x-5 \right)$ is $f\left( x \right)=\left( {{x}^{3}}-3{{x}^{2}}-13x+15 \right)$.

Note: While answering questions of this type we should be sure with our calculations. This is a very simple and easy question and it can be solved in a short span of time. We just need to perform simple basic arithmetic operations like addition, subtraction and multiplication for solving questions of this type. The conclusion should be as simple as it is possible. We can also simplify and expand any similar expression function like we will simplify this expression $g\left( x \right)=\left( x-3 \right)\left( x+2 \right)$ and then we will have this as result $g\left( x \right)=\left( x-3 \right)\left( x+2 \right)\Rightarrow g\left( x \right)={{x}^{2}}-x-6$ .