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Sagot :
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.
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.
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