Addition of polynomials can be solved in two methods.

(i) By arranging the like terms together and then add.

For example:

1. Add: 5x + 3y, 4x – 4y + z and -3x + 5y + 2z

First we need to write in the addition form.

= (5x + 3y) + (4x – 4y + z) + (-3x + 5y + 2z)

= 5x + 3y + 4x – 4y + z - 3x + 5y + 2z

Now we need to arrange all the like terms and then all the like terms are added.

= 5x + 4x - 3x + 3y – 4y + 5y + z + 2z

= 6x + 4y + 3z

2. Add: 3a2 + ab – b2, -a2 + 2ab + 3b2 and 3a2 – 10ab + 4b2

First we need to write in the addition form.

= (3a2 + ab – b2) + (-a2 + 2ab + 3b2) + (3a2 – 10ab + 4b2)

= 3a2 + ab – b2 - a2 + 2ab + 3b2 + 3a2 – 10ab + 4b2

Here, we need to arrange the like terms and then add

= 3a2 - a2 + 3a2 + ab + 2ab – 10ab – b2 + 3b2 + 4b2

= 5a2 – 7ab + 6b2

(ii) By arranging expressions in lines so that the like terms with their signs are one below the other i.e. like terms are in same vertical column and then add the different groups of like terms.

For example:

1. Add: 7a + 5b, 6a – 6b + 3c and -5a + 7b + 4c First we will arrange the three expressions one below the other, placing the like terms in the same column.Now the like terms are added by adding their coefficients with their signs.

Therefore, adding 7a + 5b, 6a – 6b + 3c and -5a + 7b + 4c is 8a + 6b + 7c.

2. Add: 3x3 – 5x2 + 8x + 10, 15x3 – 6x – 23, 9x2 – 4x + 15 and -8x3 + 2x2 – 7x. First we will arrange the like terms in the vertical column and then the like terms are added by adding their coefficients with their signs.
Therefore, adding 3x3 – 5x2 + 8x + 10, 15x3 – 6x – 23, 9x2 – 4x + 15 and -8x3 + 2x2 – 7x is 10x3 + 6x2 – 9x + 2.

Thus, we have learnt how to solve addition of polynomials in both the methods.

Types of Algebraic Expressions

Degree of a Polynomial

Subtraction of Polynomials

Power of Literal Quantities

Multiplication of Two Monomials

Multiplication of Polynomial by Monomial

Multiplication of two Binomials

Division of Monomials