Question

Evaluate the expression $15-\left[10+{\left(3-2\right)}^2\right]+6$.

Short answer

The simplification expression of $15-\left[10+{\left(3-2\right)}^2\right]+6$is 10.

Step-by-step solution

Step 1. Apply the BODMAS rule.

According to the BODMAS rule of simplification, at first, the bracket operation must be completed followed by multiplication, addition, and then subtraction.

Step 2. Example of applying BODMAS rule.

The expression $2+[10-{(3+1)}^2]-10$can be written as

$\begin{array}{l}2+[10-{\left(3+1\right)}^2]-10=2+[10-4^2]-10\\ =2+[10-16]-10\\ =2-6-10\\ =2-16\\ =-14\end{array}$

Step 3. DESCRIPTION OF STEP.

The expression $15-\left[10+{\left(3-2\right)}^2\right]+6$can be simplified as follows:

$\begin{array}{l}15-\left[10+{\left(3-2\right)}^2\right]+6\\ =15-\left[10+{\left(1\right)}^2\right]+6\\ =15-11+6\\ =15+6-11\\ =21-11\\ =10\end{array}$

Hence, the simplified expression $15-\left[10+{\left(3-2\right)}^2\right]+6$is 10.