Sure, let's break down the problem step-by-step to simplify the expression [tex]\( -2 \times (3 + 8 \div 4)^2 \)[/tex].
1. Simplify Inside the Parentheses:
First, we need to evaluate the expression inside the parentheses: [tex]\( 3 + 8 \div 4 \)[/tex].
- We start with the division: [tex]\( 8 \div 4 \)[/tex] which equals [tex]\( 2 \)[/tex].
- Next, we add [tex]\( 3 + 2 \)[/tex], resulting in [tex]\( 5 \)[/tex].
So, [tex]\( 3 + 8 \div 4 \)[/tex] simplifies to [tex]\( 5 \)[/tex].
2. Evaluate the Outer Expression:
Now we substitute the simplified term back into the original expression: [tex]\( -2 \times (5)^2 \)[/tex].
- First, we need to square [tex]\( 5 \)[/tex]. So, [tex]\( 5^2 \)[/tex] equals [tex]\( 25 \)[/tex].
- Next, we multiply by [tex]\( -2 \)[/tex]: [tex]\( -2 \times 25 \)[/tex].
3. Final Calculation:
Performing the multiplication, [tex]\( -2 \times 25 \)[/tex] equals [tex]\( -50 \)[/tex].
Hence, the simplified result of the expression [tex]\( -2 \times (3 + 8 \div 4)^2 \)[/tex] is [tex]\( -50 \)[/tex].
