# 2a-{6b-4[a-(b-3a)] }I tried just working within the brackets first, but my answer was still wrong.

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Distribute the negative into the (b-3a), so it becomes:

2a - {6b - 4[a - b +3a] then combine like terms in the brackets:

2a - {6b - 4[4a - b]} then distribute the -4 into the square brackets:

2a - {6b -16a + 4b} then combine like terms inside {}

2a - {10b - 16a} then distribute - into {}

2a - 10b + 16a finally, combine like terms 18a - 10b

In solving problems like this start by removing the innermost brackets first and then proceed towards removing outward brackets. Thus in this example the first bracket to be removed will be represented by (). This will be followed by the bracket represented by []. Finally the bracket represented by {} will be removed.

In removing bracket if a negative sign precedes the whole bracket, then sign of all the term in the bracket will be reversed. Also if the bracket is multiplied by a negative term then sign of the products will be reversed.

Using these rules we simplify the given expression as follows:

2a - {6b -4[a - (b - 3a)]}

= 2a - {6b - 4[a - b + 3a]}

= 2a - {6b - 4a + 4b - 12a}

= 2a - 6b + 4a - 4b + 12a

= 18a - 10b

2a-{6b-4[a-(b-3a)] }

For any question to be solved the rule of BODMAS is to be followed. With smallest brackets being solved at first, and so on.

Therefore, on opening the innermost brackets, by multiplying each term by minus sign outside the bracket we get:

2a-{6b-4[a-b+3a]}

2a-{6b-4[4a-b]}

Now opening the second bracket bu multiplying each term inside bracket by 4:

2a-{6b-16a+4b}

2a-{10b-16a}

Opening the curly brackets:

2a-10b+16a

18a-10b

Taking common:

=**2(9a-5b)**

2a-{6b-4[a-(b-3a)] }

get rid of the parentheses

2a-{6b-4[a-b-3a] }

Combine the numbers in the bracket

2a-{6b-4[4a-b] }

now get rid of the [] by distributing the -4 in front

2a-{6b-16a+4b}

combine like terms again:

2a-{10b-16a}

now get rid of the {} by distributing the - in front of it

2a-10b+16a

combine like terms for one last time

18a-10b

you can farther simplify this by factoring out the greatest common factor which would be 2

2 ( 9a-5b )

For this, you have to remove the inner brackets first. Then, you move onto the larger brackets, until there are none, and then go onto the rest.

So, for this question, you have to work out (b-3a), but this is impossible, because b and a are different variables. So, you move onto the next, which is [a-(b-3a)]. If you remove the inner brackets, this equals to [a-b+3a], because -(-3a) is +3a. This will equal to [4a-b]

Then move onto 4[4a-b]. You have to multiply 4 to 4a and -b, and the result will be [16-4b]

to move onto the largest bracket, you solve the equasion as before. {6b-(16a-4b)}, and this will be {6b-16a+4b}

Then, the last part; 2a-6b+16a-4b

This will be 18a-10b.

To simplify, 18a-10b=2(9a-5b)

so:

2a-{6b-4[a-(b-3a)] }

=2a-{6b-4[4a-b]}

=2a-{6b-16a+4b}

=2a-{10b-16a}

= 2a-10b+16a

=18a-10b

=2(9a-5b)