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Simplify -(8m)-(-7m+2)

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In the early days, people use to do calculations by counting their fingers for addition and subtraction. Later they get to know about mathematical operations like addition, subtraction, multiplication, and division. They can easily calculate the numerical problem by using operators. Then later, some instances came they have to suppose things in mathematics and have to get the exact value of what they have supposed. That was not easy for calculation so they supposed it as alphabetical letters and assume it is required. They apply all the arithmetic operation which was required to get the value and this process is termed algebra. So we can say ‘Algebra is the study of unknowns.’

Algebraic Expression

An algebraic expression is the combination of numerals, variables, and operators. An algebraic expression is the mathematical representation of the mathematical statement. For example, if we have to represent the ‘ three times a number increased by 4’ in mathematics then it can be written as ‘ 3x +4 ‘. In ‘3x + 4’, + sign divide the expression in two terms. 

On the basis of the number of terms, an algebraic expression is divided into the following parts.

  • Monomial: If the number of terms in an algebraic expression is one then we call it a monomial. Example: 9x, 6y, etc
  • Binomial: If the number of terms in algebraic expression is two then the algebraic expression is known as binomial. Example: 5x+9, 9y+3, etc
  • Trinomial: If the number of terms in an algebraic expression is three then we call it trinomial. Example: 8a+2c-9, 8y-6z+3, etc
  • Polynomial: If the number of terms in an algebraic expression is one or more than one then it is called a polynomial. Example: 5x, 6c+8d, 9t-6u+2w, etc

We do all the arithmetic operations on the like term of the algebraic expression. So let’s have a look at like and unlike terms.

Like and unlike terms: 

If the variable part of the algebraic expression is the same then it is known as the like term and if the variable part is not the same then it is called the unlike term.

Example: 5x² + 9xy + 8y +2x² +6z -xy

In the above algebraic expression, the variable part of 5x² and 2x² is the same and the variable part of 9xy and xy is the same. So they are like terms.

Operations on algebraic expression:

  1. Addition: If there is +ve sign between two like terms then we can easily add the numerals part the like terms and write them in a single term.
  2. Subtraction: If there is -ve sign between two like terms then we can easily subtract them.
  3. Multiplication: Multiplication can be done for like and unlike terms both.
  4. Division: Division of two-like terms can be done easily because they can be easily cancelled out but the division of unlike terms is written in the same way as it is.

Simplify -(8m)-(-7m+2)

Solution: 

Step 1: Open the bracket by using the distributive property of subtraction i.e. {(x+y)-(a-b) = x + y -a +b}

Multiplication of (-)ve with (-)ve, (+)ve with (+)ve is (+)ve, and multiplication of (-)ve with (+)ve is (-)ve.  

= -8m – (-7m) -2

= -8m + 7m -2

Step 2: Apply the arithmetic operation on the like terms.

= -m -2

Step 3: Take out the common part and write the expression in the simplest form.

Here in the question, we can see the negative sign is common in both terms.

= -(m+2)

So the simplification of -(8m)-(-7m+2) is -(m+2).

Similar Questions

Question 1: Simplify :- 3y – ( 5y -3)

Solution: 

Open the bracket by using the distributive property of subtraction i.e. {(x+y)-(a-b) = x + y -a +b}

Multiplication of (-)ve with (-)ve, (+)ve with (+)ve is (+)ve, and multiplication of (-)ve with (+)ve is (-)ve.  

= 3y -(5y) -(-3)

=3y – 5y + 3

Apply the arithmetic operation on the like terms.

= -2y + 3

=3 -2y 

So the simplification of  3y – ( 5y -3) is 3 -2y

Question 2: Simplify:- (9x +2z) – (-3x +5z -2)

Solution: 

Open the bracket by using the distributive property of subtraction i.e. {(x+y)-(a-b) = x + y -a +b}

Multiplication of (-)ve with (-)ve, (+)ve with (+)ve is (+)ve, and multiplication of (-)ve with (+)ve is (-)ve.  

= 9x + 2z – (-3x) -(5z) -(-2)

= 9x +2z +3x -5z +2

Apply the arithmetic operation on the like terms

= 9x + 3x + 2z -5z +2

= 12x -3z +2

So the simplification of (9x +2z) – (-3x +5z -2) is 12x -3z +2.


Last Updated : 25 Dec, 2023
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