Addition of polynomials can be solved in two methods.
(i) By arranging the like terms together and then add.
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
(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.
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.
Thus, we have learnt how to solve addition of polynomials in both the methods.
● Terms of an Algebraic Expression
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