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To solve the expression \( 49 - (m - 3)^2 \) using arithmetic and applying formulas, we will approach this step-by-step:

### Step 1: Apply the Binomial Formula
The expression inside the square is \( (m - 3)^2 \), which expands using the binomial square formula:
\[
(a - b)^2 = a^2 - 2ab + b^2
\]
Here, \( a = m \) and \( b = 3 \). Thus, expanding \( (m - 3)^2 \) gives:
\[
(m - 3)^2 = m^2 - 6m + 9
\]

### Step 2: Substitute Back Into the Original Expression
Now, substitute this expansion back into the original expression \( 49 - (m - 3)^2 \):
\[
49 - (m^2 - 6m + 9)
\]
Distribute the negative sign:
\[
49 - m^2 + 6m - 9
\]

### Step 3: Simplify the Expression
Now, combine like terms:
\[
49 - 9 = 40
\]
So, the expression simplifies to:
\[
40 + 6m - m^2
\]

Thus, the simplified form of the expression is:
\[
40 + 6m - m^2
\]

Would you like more details or have any questions about this process?

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Here are 5 related questions to expand your understanding:
1. How would the process change if the expression had \( (m + 3)^2 \) instead?
2. What is the significance of the binomial square formula in algebraic expansions?
3. How would you factorize the final expression \( 40 + 6m - m^2 \)?
4. Can this expression be solved for specific values of \( m \)?
5. How would this expression change if you introduced a different constant inside the binomial term?

**Tip:** When simplifying expressions involving squares, always expand carefully using binomial formulas to avoid errors in signs and terms.

Learn how to simplify the expression 49 - (m - 3)^2 using the binomial expansion formula. This step-by-step explanation involves expanding binomial squares and simplifying the result, suitable for students in Grades 8-10.

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