Addition of Polynomials
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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
= 5x + 4x - 3x + 3y – 4y + 5y + z + 2z
= 6x + 4y + 3z
2. Add: 3a2 + ab – b2, -a2 + 2ab + 3b2 and 3a2 – 10ab + 4b2
= (3a2 + ab – b2) + (-a2 + 2ab + 3b2) + (3a2 – 10ab + 4b2)
= 3a2 + ab – b2 - a2 + 2ab + 3b2 + 3a2 – 10ab + 4b2
= 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. Ida'amni 3x3 – 5x2 + 8x + 10, 15x3 – 6x – 23, 9x2 – 4x + 15 fi -8x3 + 2x2 – 7x.
Kanaafuu 3x3 – 5x2 + 8x + 10, 15x3 – 6x – 23, 9x2 – 4x + 15 and -8x3 + 2x2 – 7x is 10x3 + 6x2 – 9x + 2.
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