Let's break down the solution for the given expression step-by-step. The expression we need to evaluate is:
[tex]\[ 4(4n - 3) - 16n + 2n(5n + 10) \][/tex]
with the value of [tex]\( n = 7 \)[/tex].
### Step 1: Substitute [tex]\( n = 7 \)[/tex]
First, let's substitute [tex]\( n = 7 \)[/tex] into the expression:
[tex]\[ 4(4 \cdot 7 - 3) - 16 \cdot 7 + 2 \cdot 7 (5 \cdot 7 + 10) \][/tex]
### Step 2: Simplify each part of the expression
Part 1: [tex]\( 4(4 \cdot 7 - 3) \)[/tex]
- Calculate inside the parentheses: [tex]\( 4 \cdot 7 = 28 \)[/tex]
- Subtract: [tex]\( 28 - 3 = 25 \)[/tex]
- Multiply by 4: [tex]\( 4 \cdot 25 = 100 \)[/tex]
So, the first part is [tex]\( 100 \)[/tex].
Part 2: [tex]\(-16 \cdot 7\)[/tex]
- Multiply: [tex]\(-16 \cdot 7 = -112 \)[/tex]
So, the second part is [tex]\(-112 \)[/tex].
Part 3: [tex]\( 2 \cdot 7 (5 \cdot 7 + 10) \)[/tex]
- Calculate inside the parentheses: [tex]\( 5 \cdot 7 = 35 \)[/tex]
- Add: [tex]\( 35 + 10 = 45 \)[/tex]
- Multiply by [tex]\( 2 \cdot 7 \)[/tex]: [tex]\( 2 \cdot 7 \cdot 45 = 14 \cdot 45 = 630 \)[/tex]
So, the third part is [tex]\( 630 \)[/tex].
### Step 3: Combine the parts to get the final result
Sum the results of all the parts:
[tex]\[ 100 + (-112) + 630 \][/tex]
- First, add [tex]\( 100 \)[/tex] and [tex]\( -112 \)[/tex]: [tex]\( 100 - 112 = -12 \)[/tex]
- Then, add [tex]\(-12\)[/tex] and [tex]\( 630 \)[/tex]: [tex]\( -12 + 630 = 618 \)[/tex]
So, the final result is [tex]\( 618 \)[/tex].
To summarize:
- Part 1: [tex]\( 100 \)[/tex]
- Part 2: [tex]\(-112\)[/tex]
- Part 3: [tex]\( 630 \)[/tex]
- Result: [tex]\( 618 \)[/tex]
Therefore, the complete and final result of the expression [tex]\( 4(4n - 3) - 16n + 2n(5n + 10) \)[/tex] when [tex]\( n = 7 \)[/tex] is [tex]\( 618 \)[/tex].
