Sure, let's multiply the two binomials [tex]\((x + 2)\)[/tex] and [tex]\((y + 3)\)[/tex] step by step to find the resulting polynomial.
1. Write the problem down:
[tex]\[
(x + 2)(y + 3)
\][/tex]
2. Apply the distributive property (FOIL method) to multiply the binomials:
- First, multiply the first terms:
[tex]\[
x \cdot y = xy
\][/tex]
- Next, multiply the outer terms:
[tex]\[
x \cdot 3 = 3x
\][/tex]
- Then, multiply the inner terms:
[tex]\[
2 \cdot y = 2y
\][/tex]
- Finally, multiply the last terms:
[tex]\[
2 \cdot 3 = 6
\][/tex]
3. Summing these products:
[tex]\[
xy + 3x + 2y + 6
\][/tex]
Thus, the result of multiplying the binomials [tex]\((x + 2)\)[/tex] and [tex]\((y + 3)\)[/tex] is:
[tex]\[
xy + 3x + 2y + 6
\][/tex]
This polynomial combines the products of each pair of terms from the original binomials.
