(2x + 5y)(3x^2 - 4xy + 2y^2)
= 6x^3 - 8xy + 4xy^2 + 15x^2y - 20xy^2 + 10y^3
Hmm. I get
2x(3x^2-4xy+2y^2) + 5y(3x^2-4xy+2y^2)
= 6x^3 - 8x^2y + 4xy^2
+ 15x^2y - 20xy^2 + 10y^3
= 6x^3 + 7x^2y - 16xy^2 + 10y^3
To expand the expression (2x + 5y)(3x^2 - 4xy + 2y^2), we need to distribute each term from the first parentheses to each term in the second parentheses. This can be done using the distributive property.
Let's break down the steps:
Step 1: Multiply 2x by each term in the second parentheses: 2x * 3x^2 = 6x^3, 2x * -4xy = -8xy, and 2x * 2y^2 = 4xy^2.
Step 2: Multiply 5y by each term in the second parentheses: 5y * 3x^2 = 15x^2y, 5y * -4xy = -20xy^2, and 5y * 2y^2 = 10y^3.
Step 3: Combine the like terms: -8xy + 4xy^2 = -4xy + 4xy^2.
Putting it all together, the expanded form of (2x + 5y)(3x^2 - 4xy + 2y^2) is:
6x^3 - 8xy + 4xy^2 + 15x^2y - 20xy^2 + 10y^3.