Addition of Polynomials

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.

Thus, the required addition

= (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.

Thus, the required addition

= (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

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. 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.

● Terms of an Algebraic Expression

Types of Algebraic Expressions

Degree of a Polynomial

Addition of Polynomials

Subtraction of Polynomials

Power of Literal Quantities

Multiplication of Two Monomials

Multiplication of Polynomial by Monomial

Multiplication of two Binomials

Division of Monomials

6th Grade Math Practice

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