The expression 5xy(2x - y) + 6y²(x² + 6) simplifies to 10x³y - 5xy² + 36y² in standard form. None of the options provided by the student match this result, indicating a potential error in the question or options.
The student is asking to write the expression 5xy(2x - y) + 6y²(x² + 6) in standard form. To simplify this expression, we need to expand the products and then combine like terms.
First, we expand the product following the distributive property:
- 5xy × 2x = 10x³y
- 5xy × (-y) = -5xy²
- 6y² × x² = 6x²y²
- 6y² × 6 = 36y²
Now we combine the like terms:
- There are no terms to combine with 10x³y, so it remains as is.
- The two terms with x²y² are -5xy² and 6x²y², which sum up to 1x²y².
- The last term is 36y².
Therefore, the expression in standard form is:
10x³y - 5xy² + 36y²
None of the given options in the question (a, b, c, and d) match this result. There may be an error in the provided options or in the original question.