Of course! Let's simplify the given expressions step-by-step.
### Expression 1: [tex]\( m(m-8) \)[/tex]
To simplify [tex]\( m(m-8) \)[/tex]:
1. Distribute [tex]\( m \)[/tex] to each term inside the parenthesis:
[tex]\[
m \cdot m - m \cdot 8
\][/tex]
2. Perform the multiplication:
[tex]\[
m^2 - 8m
\][/tex]
Thus, the simplified form of [tex]\( m(m-8) \)[/tex] is:
[tex]\[
m^2 - 8m
\][/tex]
### Expression 2: [tex]\( (m+8)(m-8) \)[/tex]
To simplify [tex]\( (m+8)(m-8) \)[/tex], we recognize it as a difference of squares.
[tex]\[
(a+b)(a-b) = a^2 - b^2
\][/tex]
Here, [tex]\( a = m \)[/tex] and [tex]\( b = 8 \)[/tex].
So, applying the difference of squares formula:
[tex]\[
(m+8)(m-8) = m^2 - 8^2
\][/tex]
Since [tex]\( 8^2 = 64 \)[/tex], we get:
[tex]\[
m^2 - 64
\][/tex]
Thus, the simplified form of [tex]\( (m+8)(m-8) \)[/tex] is:
[tex]\[
m^2 - 64
\][/tex]
### Expression 3: [tex]\( (m+7)(m-3) \)[/tex]
To simplify [tex]\( (m+7)(m-3) \)[/tex]:
1. Use the distributive property (also known as FOIL method for binomials):
[tex]\[
(m+7)(m-3) = m(m-3) + 7(m-3)
\][/tex]
2. Distribute [tex]\( m \)[/tex] and [tex]\( 7 \)[/tex] to each term inside the parenthesis:
[tex]\[
m \cdot m - m \cdot 3 + 7 \cdot m - 7 \cdot 3
\][/tex]
3. Perform the multiplication:
[tex]\[
m^2 - 3m + 7m - 21
\][/tex]
4. Combine like terms:
[tex]\[
m^2 + 4m - 21
\][/tex]
Thus, the simplified form of [tex]\( (m+7)(m-3) \)[/tex] is:
[tex]\[
m^2 + 4m - 21
\][/tex]
### Summary:
- [tex]\( m(m-8) = m^2 - 8m \)[/tex]
- [tex]\( (m+8)(m-8) = m^2 - 64 \)[/tex]
- [tex]\( (m+7)(m-3) = m^2 + 4m - 21 \)[/tex]
So, the simplified forms of the given expressions are:
[tex]\[
(m^2 - 8m, m^2 - 64, m^2 + 4m - 21)
\][/tex]
