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How do you simplify #3(2b-a)-(2a-b)#?

Answer 1

Julia Adams

#color(darkblue)(7b-5a)#

Simplify by distributing.

First take #3# and multiply it across the first binomial, which is #2b-a#.

#color(orange)3(color(green)(2b)-color(red)a) = (color(orange)3)(color(green)(2b)) - (color(orange)3)(color(red)a)#

Now simplify.

#color(blue)(6b) - color(blue)(3a)#

At this point, we have simplified as much as possible in the first parentheses. We can move on to the #(2a-b)#.

There is a subtraction sign in between the two binomials, so we can take that and distribute it across as a negative sign. Remember: #x - y = x + -y#.

#color(blue)(6b-3a) - color(purple)(2a+b)#

Now combine like terms.

#color(darkblue)(7b-5a)#

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Answer 2

Abigail Allen

To simplify the expression 3(2b-a) - (2a-b), distribute the 3 to each term inside the parentheses:

3 * 2b = 6b 3 * (-a) = -3a

Then, distribute the negative sign to each term inside the second set of parentheses:

-(2a) = -2a -(-b) = +b

Now, combine like terms:

6b - 3a - 2a + b

Combine like terms with the same variables:

6b + b - 3a - 2a

Combine like terms:

7b - 5a

So, the simplified expression is 7b - 5a.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.