Question

simply the following polynomials
9. (4m+n)(m-2n)
13.(x+3)^2
14(a-3)^2
15 (4m+1)^2

Answer 1

Let's simplify each polynomial one by one:

9. **(4m+n)(m-2n)**
Using the distributive property (also known as the FOIL method for binomials):
\[
(4m+n)(m-2n) = 4m \cdot m + 4m \cdot (-2n) + n \cdot m + n \cdot (-2n)
\]
\[
= 4m^2 - 8mn + nm - 2n^2
\]
Combining like terms:
\[
= 4m^2 - 7mn - 2n^2
\]

13. **(x+3)^2**
Using the formula \((a + b)^2 = a^2 + 2ab + b^2\):
\[
(x+3)^2 = x^2 + 2 \cdot x \cdot 3 + 3^2
\]
\[
= x^2 + 6x + 9
\]

14. **(a-3)^2**
Using the same formula:
\[
(a-3)^2 = a^2 - 2 \cdot a \cdot 3 + 3^2
\]
\[
= a^2 - 6a + 9
\]

15. **(4m+1)^2**
Again using the formula:
\[
(4m+1)^2 = (4m)^2 + 2 \cdot (4m) \cdot 1 + 1^2
\]
\[
= 16m^2 + 8m + 1
\]

Final simplified results:
1. \(4m^2 - 7mn - 2n^2\)
2. \(x^2 + 6x + 9\)
3. \(a^2 - 6a + 9\)
4. \(16m^2 + 8m + 1\)