Final answer:
To expand and simplify the expression, distribute the coefficients to each term within the parentheses and then combine like terms. Therefore, the expanded and simplified form of 2a(a+1)+5(3a-2) is 2a^2 + 17a - 10.
Step-by-step explanation:
To expand and simplify the expression 2a(a+1)+5(3a-2), we can distribute the coefficients to each term within the parentheses and then combine like terms. The distributive property allows us to multiply each term inside the parentheses by the coefficients outside. Here are the steps:
- Multiply 2a by (a+1): 2a x a = 2a^2 and 2a x 1 = 2a
- Multiply 5 by (3a-2): 5 x 3a = 15a and 5 x -2 = -10
- Combine the terms: 2a^2 + 2a + 15a - 10
- Collect like terms: 2a^2 + (2a + 15a) - 10
- Combine the coefficients: 2a^2 + 17a - 10
Therefore, the expanded and simplified form of 2a(a+1)+5(3a-2) is 2a^2 + 17a - 10.