Expand and simplify the following expression.a 5ab(3a+5b )-2a(3ab-4b)
5ab(3a+5b )-2a(3ab-4b)
5ab*3a + 5ab*5b - 2a*3ab + 2a*4b
...
8a – 5b – 3 – 2a + 5 – 4b
To expand and simplify the expression 5ab(3a + 5b) - 2a(3ab - 4b), we will first distribute the terms within parentheses, and then combine like terms.
Let's start with the first term: 5ab(3a + 5b). To distribute 5ab to both terms inside the parentheses, we multiply 5ab by 3a and by 5b separately:
5ab * 3a = 15a^2b
5ab * 5b = 25ab^2
So, the expression becomes: 15a^2b + 25ab^2.
Now let's move on to the second term: -2a(3ab - 4b). Similar to before, we distribute -2a to both terms inside the parentheses:
-2a * 3ab = -6a^2b
-2a * -4b = 8ab
Thus, the second term simplifies to: -6a^2b + 8ab.
Finally, we combine the terms we obtained from distributing both terms:
(15a^2b + 25ab^2) - (6a^2b - 8ab)
When we subtract the second term (distribute the negative sign), it changes the sign of every term in the second term:
15a^2b + 25ab^2 - 6a^2b + 8ab
Now, we can combine the like terms, which are terms that have the same variables raised to the same powers:
(15a^2b - 6a^2b) + (25ab^2 + 8ab)
The like terms simplify to:
9a^2b + 33ab^2
Therefore, the expanded and simplified expression is 9a^2b + 33ab^2.