Solve this: (5n-2)(2n+6)-(n-2)(3n+2)
"solving" needs an equation, you probably meant
simplify (5n-2)(2n+6)-(n-2)(3n+2)
= 10n^2 + 30n - 4n - 3n^2 - 2n + 6n + 4
= .......
3n+2=2n+4
To solve the given expression, (5n-2)(2n+6)-(n-2)(3n+2), we need to simplify and combine like terms.
First, we can expand both sets of parentheses using the distributive property.
For the first set of parentheses, (5n-2)(2n+6), we multiply each term inside the first parentheses by each term inside the second parentheses:
(5n) * (2n) + (5n) * (6) - (2) * (2n) - (2) * (6)
Simplifying this, we get:
10n^2 + 30n - 4n - 12
Next, we expand the second set of parentheses, (n-2)(3n+2):
(n) * (3n) + (n) * (2) - (2) * (3n) - (2) * (2)
Simplifying this, we get:
3n^2 + 2n - 6n - 4
Now, let's put both expressions together and combine like terms:
(10n^2 + 30n - 4n - 12) - (3n^2 + 2n - 6n - 4)
Removing the parentheses and simplifying the expression further, we have:
10n^2 + 30n - 4n - 12 - 3n^2 - 2n + 6n + 4
Next, we combine the like terms:
(10n^2 - 3n^2) + (30n - 4n + 6n) + (-12 + 4)
Finally, combining further, we get:
7n^2 + 32n - 8
Therefore, the solution to the given expression (5n-2)(2n+6)-(n-2)(3n+2) is 7n^2 + 32n - 8.