Substitution and Evaluation of Expressions

Example on substituting and evaluating expressions

Example 1


What is the value of $(-x^3 + y^2)-2( - x^2 - y^3 )$ for $x = - 2$ and $y = - 3$ ?

  1. $9$
  2. $-9$
  3. $-29$
  4. $29$
  5. $-30$

Solution

This example is about substitution in and evaluation of algebraic expressions.

  1. According to the $5$ possible answers, we need to evaluate the given expression by substituting $x$ by $\color{red}{(-2)}$ and $y$ by $\color{blue}{(-3)}$ in the given algebraic expression as follows:(NOTE the use of parentheses)

    $(-x^3 + y^2)-2( - x^2 - y^3 )= (-\color{red}{(-2)}^3 +\color{blue}{(-3)}^2)-2( - \color{red}{(-2)}^2 - \color{blue}{(-3)}^3 )$


  2. Simplify (you may use the calculator at this point)

    $=(-(-8) +9)-2( - 4 - (-27) )$

    $=(8+9)-2(-4+27)$

    $=17-2(23)$

    $=17-46$

    $=-29$

    Answer C