(2a+4b)-(3a-b)when and how do u know to change the signs?
It might help to think of it as below.
(2a+4b)-1(3a-b)
Mutliply the last term by the -1.
2a+4b-3a+b = -a+5b or 5b-a
I hope this helps. Thanks for asking.
To simplify the expression (2a+4b)-(3a-b), you need to distribute the negative sign to every term inside the parentheses. This can be done by multiplying each term by -1.
So, (2a+4b)-(3a-b) becomes:
2a + 4b - 1(3a) - 1(-b)
Now, when multiplying by a negative number, you need to change the signs of each term.
So, -1(3a) becomes -3a, and -1(-b) becomes +b.
Therefore, the expression simplifies to: 2a + 4b - 3a + b.
Now, you can combine like terms: 2a - 3a + 4b + b.
-3a and 2a have the same variable "a" with opposite signs (-3 and +2), so you subtract them: -3a - 2a = -5a.
Similarly, 4b and b have the same variable "b", so you add them: 4b + b = 5b.
Putting it all together, the simplified expression is: -5a + 5b, or you can also write it as 5b - 5a.
By changing the signs when multiplying by -1, you ensure that you are subtracting the terms enclosed in the parentheses properly.