𝟐𝒙+𝟑𝒚 কে 𝟑𝒙+𝟐𝒚 দ্বারা গুণ করলে গুণফল কত?6𝑥2+13𝑥𝑦−6𝑦26x 2 +13xy−6y 2 6𝑥2+13𝑥𝑦+5𝑦26x 2 +13xy+5y 2 6𝑥2+13𝑥𝑦+6𝑦26x 2 +13xy+6y 2 6𝑥2+13𝑥𝑦+6𝑦26x 2 +13xy+6y 2

1. Break Down the Problem

We need to multiply the two expressions $2x + 3y$ and $3x + 2y$ and find the resulting polynomial.

2. Relevant Concepts

To multiply two binomials, we use the distributive property (also known as the FOIL method for binomials).

3. Analysis and Detail

We'll calculate the product step by step:

1. Multiply the first terms: $2x \cdot 3x = 6x^2$

2. Multiply the outer terms: $2x \cdot 2y = 4xy$

3. Multiply the inner terms: $3y \cdot 3x = 9xy$

4. Multiply the last terms: $3y \cdot 2y = 6y^2$

5. Combine all the terms: $6x^2 + 4xy + 9xy + 6y^2 = 6x^2 + (4xy + 9xy) + 6y^2 = 6x^2 + 13xy + 6y^2$

4. Verify and Summarize

The result of multiplying the two expressions is: $6x^2 + 13xy + 6y^2$

Final Answer

The product of $2x + 3y$ and $3x + 2y$ is: $6x^2 + 13xy + 6y^2$