(7a+5b)−(5a−7b) = I do not know the method to answering this question.

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embizze's profile pic

embizze | High School Teacher | (Level 1) Educator Emeritus

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First, you want to look at the instructions for the problem or set of problems. Look for the words evaluate, simplify, or solve. These are the key words that tell you what actions to take and the form of your answer.

If the instructions are to evaluate then you will be given an input number or expression. You will then substitute (plug in) the given value. Then perform the arithmetic operations to arrive at an answer. The answer will be an expression, usually be in the form of a number. For example evaluate the expression x^2 at x=-2; the result is (-2)^2=4. Another example is to evaluate 2xy at x=3; the result is 2(3)y=6y.

If the instruction is to simplify, the answer will be an expression, sometimes a number. Here you use the order of operations to reduce the given expression. For example simplify 3x^2-2(x^2+x); first eliminate the parantheses using the distributive property to get 3x^2-2x^2-2x; then add like terms to get x^2-2x.

Finally, if the instructions are to solve then you will be given an equation or inequality. The answer will be in the form of a set of numbers that satisfy the given conditions. (Note the difference -- evaluating and simplifying yield expressions and solving has solutions.) For example, solve 2x=x+3; subtracting x from both sides gives x=3 which is the only solution.


For your problem I suspect the instructions are to simplify the given expression. Use the order of operations:

(7a+5b)-(5a-7b): Use the distributive property

(7a+5b)-5a+7b  Note that -(-7b) is 7b (read as the opposite of the opposite of 7b.)

Now the first set of parantheses can be dropped to get:

7a+5b-5a+7b Now add like terms to get:

2a+12b which is the answer to your problem.


7a+5b-5a+7b Use the commutative property of addition

7a-5a+5b+7b Now use the distributive property

(7-5)a+(5+7)b Evaluate the expressions in the parantheses

2a+12b as above.

malkaam's profile pic

malkaam | Student, Undergraduate | (Level 1) Valedictorian

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To solve this you can either follow the BODMAS or PEMDAS,

(7a + 5b) - (5a - 7b)

First we need to check that can we solve within the brackets, the answer here is no because only similar terms can be added or subtracted, so we need to open the brackets,

(7a + 5b) - (5a - 7b)

7a + 5b - 5a + 7b    

(the sign of 5a became minus and the sign of 7b became plus, because different signs when multiplied become minus and similar signs when multiplied become plus) 

Arrange them so that similar terms are written together and it is easier to solve then add or subtract,

7a - 5a + 5b + 7b

2a + 12b Answer.

PrunTuns's profile pic

PrunTuns | (Level 1) Honors

Posted on

You'll want to first reference PEMDAS (Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction). Notice that the problem has two sets of parenthesis. They have to be addressed somehow. There are no exponents, so therefore, moving onto Multiplication of PEMDAS, we distribute that subtraction sign in the middle of the two sets of terms: 




Noting that there is no Division involved, Add the like terms, a and b: 




Because we've simplified the original problem as much as we could, the final expression is 2a+12b. 

nisarg's profile pic

nisarg | Student, Grade 11 | (Level 1) Valedictorian

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This is your problem so the first step is to move the negative sign into the parenthesis


Now you want to put like numbers and variables together


now you simply add with order of operations



ccbbrenes's profile pic

ccbbrenes | eNotes Newbie

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First you must distribute the negative sign through out the second set of parenthesis:


Now you combine the a terms:

7a-5a= 2a

Then the b terms:

5b+7b= 12b

then add those two answers together to get a final answer of:


sid-sarfraz's profile pic

sid-sarfraz | Student, Graduate | (Level 2) Salutatorian

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In this problem we have to simplify the equation till it cannot be simplified further. "a" and "b" are separate values that cannot be added, hence;


Open the brackets, Multiply minus sign to both values, this will change the signs of both digits;

= 7a + 5b - 5a + 7b

= 7a - 5a + 5b + 7b

= 2a +12b

Hence the answer is `2a+12b`


atyourservice's profile pic

atyourservice | Student, Grade 11 | (Level 3) Valedictorian

Posted on

The first step of this problem is to distribute the negative sign. Because it is in front of the (5a-7b) it means that, you multiply everything in that parenthesis by the negative sign.

This means that : (7a+5b)−(5a−7b) becomes (7a+5b)−5a+7b
The reason the - became a + is because a negative x a negative = positive
After spreading the - you can get rid of the parenthesis
7a + 5b - 5a + 7b
you can't add the a terms and the b terms because they have different exponents, so you add the terms that are alike, so the As with the As and the Bs with the Bs
7a - 5a + 5b + 7b
add like normal:
2a + 12b is the answer.

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