While adding, similar terms are grouped together and each set of similar terms is simplified to a single term.
Example 1 of Adding Polynomials :
Add 5x2 + 3x - 7 and 2x2 - 4x + 9
Solution to Example 1 of Adding Polynomials: The sum of the given Expressions = (5x2 + 3x - 7) + (2x2 - 4x + 9) Grouping similar terms, we get sum = (5x2 + 2x2) + (3x - 4x ) + (-7 + 9) = (5 + 2)x2 + (3 - 4)x + (2) = 7x2 - x + 2 Ans. The above method of adding is called horizontal method.
We can also follow another method called column method in whichaddition can be done quickly, accurately and easily.
Step 1: First write the Expressions in descending order, if they are not already there in that order.Here the given polynomials are already in descending order.
Step 2: Now write down one expression below the other in order and then add. 5x2 + 3x - 7 2x2 - 4x + 9 ------------------ 7x2 - x + 2 Ans. ------------------
Example 2 of Adding Polynomials :
Add the following Expressions by column method. 5x3 - 3x + 4 and -9x3 + 12x2 -3
Solution to Example 2 of Adding Polynomials : Step 1: First write the Expressions in descending order.If any term is missing write the coefficient 0 for it.Here first Expression does not have x2 term. So take it as 0.x2. Similarly second Polynomial does not have x term. So take it as 0.x.
Step 2: Now write down one Expression below the other in order and then add. 5x3 + 0.x2 - 3x + 4 -9x3 + 12x2 + 0.x - 3 ----------------------------- -4x3 + 12x2 - 3x + 1. Ans. -----------------------------
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Subtraction is similar to addition, except that the signs of the termsof the Expression to be subtracted are to be changed.
Example 3 of Adding Polynomials :
Take the two Expressions in Example 1 and subtract the second from the first by (i) horizontal method and (ii) column method.
Solution: Let The two Expressions be denoted by A and B. Then A = 5x2 + 3x - 7 and B = 2x2 - 4x + 9. A - B = (5x2 + 3x - 7) - (2x2 - 4x + 9) = (5x2 + 3x - 7) - 2x2 + 4x - 9 = (5x2 - 2x2) + (3x + 4x) + (-7 -9) = 3x2 + 7x -16. Ans. In column method, we follow the same procedure as in addition aboveexcept that the signs of the terms of the expression to be subtracted(written at the bottom) are changed. 5x2 + 3x - 7 2x2 - 4x + 9 (-) (+) (-) ----------------- 3x2 + 7x - 16 Ans. -----------------
Example 4 Adding Polynomials :
Take the two Expressions in Example 2 and subtract the second from the first by column method.
Solution: We have to write the second Polynomial below the first after arranging in descending order and puttiing 0 as coefficient for the missing terms as done in case of addition.
Then we have to change the signs of the terms of the bottom Polynomial and then add.
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