Let's simplify the given expression step-by-step. The given expression is:
[tex]\[
-10(-10h + 5) + 3(-3h + 7)
\][/tex]
### Step 1: Distribute the coefficients inside the parentheses
First, we distribute the [tex]\(-10\)[/tex] through the terms inside the first set of parentheses:
[tex]\[
-10 \cdot -10h + (-10) \cdot 5
\][/tex]
Calculating each term separately:
[tex]\[
-10 \cdot -10h = 100h
\][/tex]
[tex]\[
-10 \cdot 5 = -50
\][/tex]
So, the expression [tex]\( -10(-10h + 5) \)[/tex] simplifies to:
[tex]\[
100h - 50
\][/tex]
Next, we distribute the [tex]\(3\)[/tex] through the terms inside the second set of parentheses:
[tex]\[
3 \cdot -3h + 3 \cdot 7
\][/tex]
Calculating each term separately:
[tex]\[
3 \cdot -3h = -9h
\][/tex]
[tex]\[
3 \cdot 7 = 21
\][/tex]
So, the expression [tex]\( 3(-3h + 7) \)[/tex] simplifies to:
[tex]\[
-9h + 21
\][/tex]
### Step 2: Combine the simplified terms
Now, let's combine all the simplified terms from both distributions:
[tex]\[
100h - 50 + (-9h + 21)
\][/tex]
This can be rewritten as:
[tex]\[
100h - 50 - 9h + 21
\][/tex]
### Step 3: Group and combine like terms
Group the terms with [tex]\(h\)[/tex] together and the constant terms together:
[tex]\[
(100h - 9h) + (-50 + 21)
\][/tex]
Combine the like terms:
[tex]\[
100h - 9h = 91h
\][/tex]
[tex]\[
-50 + 21 = -29
\][/tex]
### Final Simplified Expression
So, the final expression in its simplest terms is:
[tex]\[
91h - 29
\][/tex]
Therefore, the simplified expression is:
[tex]\[
91h - 29
\][/tex]
