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
 |
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.
 |
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. |
Thus, we have learnt how to solve addition of polynomials in both the methods.
● Terms of an Algebraic Expression
Types of Algebraic Expressions
Multiplication of Two Monomials
Multiplication of Polynomial by Monomial
Multiplication of two Binomials
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