Final answer:
To simplify the expression -5xy(6xy^3-4xy+7y^2), we distribute -5xy across each term inside the parenthesis, resulting in -30x^2y^4 + 20x^2y^2 - 35xy^3, which is the simplified form.
Step-by-step explanation:
The question asks how to simplify the algebraic expression -5xy(6xy^3-4xy+7y^2). The first step is to distribute the term -5xy across each term inside the parenthesis. The process of distribution will involve multiplying both the coefficients and the variables, combining like terms where possible.
The simplified form will then be:
- -5xy × 6xy^3 = -30x^2y^4
- -5xy × (-4xy) = 20x^2y^2
- -5xy × 7y^2 = -35xy^3
After distribution, we combine the results:
-30x^2y^4 + 20x^2y^2 - 35xy^3