Multiply the following expressions:

1. [tex](2x^3y^3)(5x^2y^8)[/tex]

2. [tex]9b^3(8b^4)(-b)[/tex]

3. [tex]3y^2(y^2 - 2y + 3)[/tex]

4. [tex](x + 3)(x - 2)[/tex]

1. ( 2 x 3 y 3 ) ( 5 x 2 y 8 ) = 2 ⋅ 5 ⋅ x 3 + 2 ⋅ y 3 + 8 = 10 ⋅ x 5 ⋅ y 11 2. 9 b 3 ( 8 b 4 ) ( − b ) = − 9 ⋅ 8 ⋅ b 3 + 4 + 1 = − 72 ⋅ b 8
3. 3 y 2 ( y 2 − 2 y + 3 ) = = 3 y 2 ⋅ y 2 − 3 y 2 ⋅ 2 y + 3 y 2 ⋅ 3 = = 3 y 2 + 2 − 6 y 2 + 1 + 9 y 2 = = 3 y 4 − 6 y 3 + 9 y 2
4. ( x + 3 ) ( x − 2 ) = x 2 − 2 x + 3 x − 6 = x 2 + x − 6

Answered by Lilith | 2024-06-10

To multiply the expressions, we apply the distributive property and combine like terms. We arrive at the final results for each multiplication, including properly handling exponents and coefficients. Each expression is simplified step-by-step for clarity.
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Answered by Lilith | 2024-12-26