To solve each of these expressions, we will use the difference of squares formula, which states that:
\[ (a - b)(a + b) = a^2 - b^2 \]
Now, let's apply this to each expression:
\((m-3) \cdot (m+3) = m^2 - 3^2 = m^2 - 9\)
\((c-7) \cdot (c+7) = c^2 - 7^2 = c^2 - 49\)
\((4x + 5a)(5a - 4)\) is not in the form of a difference of squares. Let's expand this expression:
\[ (4x + 5a)(5a - 4) = 4x \cdot 5a - 4 \cdot 4x + 5a \cdot 5a - 5a \cdot 4 \] \[ = 20ax - 16x + 25a^2 - 20a \] So, the result is \(20ax - 16x + 25a^2 - 20a\).
\((7x-2) \cdot (7x+2) = (7x)^2 - 2^2 = 49x^2 - 4\)
\((8b + 5a)(5a - 8b)\) is also not in the difference of squares form, so we will expand this as well:
\[ (8b + 5a)(5a - 8b) = 8b \cdot 5a - 8b \cdot 8b + 5a \cdot 5a - 5a \cdot 8b \] \[ = 40ab - 64b^2 + 25a^2 - 40ab \] \[ = 25a^2 - 64b^2 \] So, the result is \(25a^2 - 64b^2\).
- \((10p-6q) \cdot (10p+6q) = (10p)^2 - (6q)^2 = 100p^2 - 36q^2\)
In summary, the simplified results are:
\(m^2 - 9\)
\(c^2 - 49\)
\(20ax - 16x + 25a^2 - 20a\)
\(49x^2 - 4\)
\(25a^2 - 64b^2\)
\(100p^2 - 36q^2\)