Question

In the following exercises , simplify the expression$(j^2-8j-27)-(j^2+2j-12)$.

Short answer

The simplified expression is $-10j-15$ .

Step-by-step solution

Step 1. Given Information .

The given expression is $\left(j^2\hspace{0.17em}-\hspace{0.17em}8j\hspace{0.17em}-\hspace{0.17em}27\right)\hspace{0.17em}-\left(j^2\hspace{0.17em}+\hspace{0.17em}2j\hspace{0.17em}-\hspace{0.17em}12\right)$ .

Step 2. Simplify  the  given expression.

Simplify the expression $\left(j^2\hspace{0.17em}-\hspace{0.17em}8j\hspace{0.17em}-\hspace{0.17em}27\right)\hspace{0.17em}-\left(j^2\hspace{0.17em}+\hspace{0.17em}2j\hspace{0.17em}-\hspace{0.17em}12\right)$

$\begin{array}{rcl}\left(j^2\hspace{0.17em}-\hspace{0.17em}8j\hspace{0.17em}-\hspace{0.17em}27\right)\hspace{0.17em}-\left(j^2\hspace{0.17em}+\hspace{0.17em}2j\hspace{0.17em}-\hspace{0.17em}12\right)& =& j^2-8j-27-j^2-2j+12\\ j^2-8j-27-j^2-2j+12& =& j^2-j^2-8j-2j-27+12\\ j^2-j^2-8j-2j-27+12& =& -10j-15\end{array}$