What is the sum of ab, a + b and b + ab?

We have been dealing with different numerals 1, 2, 3, 4 , ….. and so on, with four fundamental operators addition, subtraction, multiplication, and division. We termed this branch ‘Arithmetic’. But when we use letters to generalize the result or to represent the unknowns then we termed it ‘Algebra’. The arithmetic properties are performed using letters and numbers. These letters represent unknowns, we termed them ‘variables’. 

Let take an example to better know algebra. Suppose we have to formalize an equation for finding the area of a rectangle. We know there is two unknown dimensions i.e. length and width. Let us assume the length of a rectangle is ‘l’ and width is ‘b’. Area of rectangle = Length × Width 

By using the algebraic terms we can represent it as.

Area of Rectangle = l × b

Algebraic Expression

An algebraic expression is the combination of numerals and variables. Suppose we have numerals and a variable. we can form different equations by using different numerals, variables, and fundamental arithmetic operators. 

For example, we have to form the algebraic equations by using x, +, and 5. Then the first expression can be written as ‘x + 5’ and one more equation can be written as ‘+5x’

In ‘x+5’ we have two terms whereas in ‘+5x’ we have only one term. Basically, the arithmetic operators separate the terms, and on the basis of the number of terms algebraic expression can be divided into the following types:

• Monomial: If the number of terms in an algebraic expression is one then it is called a monomial. Example: 5x, 6y, etc
• Binomial: If the number of terms in an algebraic expression is two then it is known as the binomial. Example: 5x+3, 9y + 7, etc
• Trinomial: If the number of terms in an algebraic term is three then it is known as the trinomial. Example: 5x+6y+9z, 2x+6y+3, etc.
• Polynomial: If the number of terms in an algebraic expression is one or more than one then it is known is polynomial.

Like terms and unlike terms:

If the variable part of two different terms is the same then it is called like terms and if the variable part is not the same then it is called, unlike terms.

Example: In the equation 9x + 2y + 3 and 6x + 5y +6z, 9x and 6x is like terms, 2y and 5y is like terms because they have the same variable. Similarly 9x and 5y, 2y and 6z, etc are not like terms because they do not have the same variable. 

Addition of algebraic expression:

For the addition of two algebraic terms, they should have like terms. If they do not have like terms then write them in the same manner along with the sign. 

Example: x and 3x can be added as 4x, but 9x and 3y do not have the same terms so that will be added as 9x + 3y.

Step to solve the problem:

Step 1: Find the terms having like terms in the given algebraic expression.

Step 2: According to the arithmetic operators, do the calculation on the numerals part of the like term.

Step 3: By solving the like terms, reduce the algebraic term in the lowest term.

Step 4: Write the unlike terms along with the sign in the final answer.

What is the sum of ab, a+b, and b+ab?

Solution:

Put the arithmetic operators of addition between the given three expressions.

= ab +(a+b) + (b+ab)

= ab +a +b +a + ab

Like term in the above expression is ab and a.

= ab + ab + a + a + b

Add the like terms.

= 2ab + 2a + b

So the sum of ab, a+b and b+ab is 2ab+2a+b . 

Similar Questions

Question 1: What is the sum of xy, y+z, and x+xy?

Solution:

Put the addition arithmetic operator between the given three expressions.

= xy + (y + z) +( x + xy)

= xy + y + z + x + xy

Like term in the above expression is xy.

= xy + xy + x + y + z

Add the like terms.

= 2xy + x + y + z

So the  sum of xy, y+z  and x+xy is  2xy + x + y + z.

Question 2: What is the sum of x²y + 3y², y² + z³, and z³ + xy?

Solution:

Put the addition arithmetic operator between the given three expressions.

= (x²y + 3y²) + (y² + z³) + (z³ + xy)

= x²y + 3y² + y² + z³ + z³ + xy

In the above expression, y² and z³ have like terms.

=  3y² + y² +  z³ + z³ + x²y + xy

Add the like terms.

= 4y² + 2z³ + x²y + xy

So, the sum of x²y + 3y², y²+z³ and z³ + xy is 4y² + 2z³ + x²y + xy