Algebra: Substitution
In this course, we will learn how to substitute values into algebraic expressions accurately using three simple steps. Students who follow these steps carefully can avoid careless mistakes when performing algebraic substitution.
Related Lessons:
Three Steps Substitution Technique
Substitution is an easy technique to master if you follow these three simple steps:
- Add brackets around each variable in the expression.
- Replace the variables inside the brackets with the given values.
- Calculate the result using a calculator to find the final answer.
Below are 2 examples on the 3 steps substitution process.
Example 1
Find the value of \(\frac{1}{x^2}+\frac{1}{x}+x+x^2\) if \(x=-3\).
Solution:
\[
\begin{align*}
\frac{1}{x^2}+\frac{1}{x}+x+x^2&=\frac{1}{\left(-3\right)^2}+\frac{1}{\left(-3\right)}+\left(-3\right)+\left(-3\right)^2\\
&=5\frac{7}{9}
\end{align*}
\]
Example 2
Find the value of \(w^2v-\left(3w\right)^2\) if \(w=-2,v=\frac{5}{2}\).
Solution:
\[
\begin{align*}
w^2v-\left(3w\right)^2&=\left(-2\right)^2\left(\frac{5}{2}\right)-\left(3\left(-2\right)\right)^2\\
&=-26
\end{align*}
\]
Watch Full Concept Breakdown
To further strengthen your understanding of the 3-step substitution technique, the video below walks through the complete concept covered above, presenting each step clearly and systematically.