Add Dissimilar Terms

Algebra Help: Section 2.4

Learn to add polynomials with algebra. Place dissimilar terms in the same columns.

Similar terms may be united as explained in section 2.2, Case 1, Add Similar Terms. It's immaterial in what order the terms are written in the sum. The whole equals the sum of all its parts, in whatever order the parts are taken. Obtain a reduced expression from the process.

Case 2

Add dissimilar terms by writing them one after another, connected by proper signs.

1. Add 3a + 2bc, 4a - 7bc+ m, and x2 - 2a + 3bc.

OPERATION

     3a + 2bc
     4a - 7bc + m
x2 - 2a + 3bc
________________________
x2 + 5a - 2bc + m

ANALYSIS - We write 3a, 4a, and - 2a, in one column, because they are similar terms. We write 2bc, - 7bc, and 3bc, in another column, for the same reason. We write x2 and m in separate columns, not being similar to each other, or to any of the other terms.

Calculate the sums, starting from the left. Write x2 in the sum. Next, write the sum of - 2a, + 4a, and + 3a, which is 5a. Write 5a under the column added. The sum of + 3bc, - 7bc, and + 2bc, is -2bc. Write -2bc under the column added. Finally annex + m, to obtain the entire sum:
x2 + 5a - 2bc + m.

From this example we deduce the following rules:

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