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Multiply the binomials: [tex](x+2)(y+3)[/tex]

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.