Addition of polynomials – Example

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Add (𝟏𝟓𝒙𝒚^𝟐𝒛 + 𝟏𝟒𝒙𝒛 + 𝟑𝒙𝒚 − 𝟏𝟎𝒚^𝟐𝒙)𝒂𝒏𝒅(𝟑 + 𝒙𝒚^𝟐𝒛 + 𝒙𝒚^𝟐 + 𝒙𝒚)using the column method.

Solution:

In the column method, write the expressions, such that the like terms are arranged in the same column.

15𝑥𝑦2𝑧	+14xz	+3xy	-10𝑦2𝑥
𝑥𝑦2𝑧		+xy	+ 𝑥𝑦2	+3

In the above arrangement, there is no term under 14xz as there is no term in the second expression with the same variables. Also, 10𝑦²𝑥 𝑎𝑛𝑑 𝑥𝑦² have the same variables with the same exponents. Hence they are like terms.

Now adding the like terms,

15𝑥𝑦2𝑧	+14xz	+3xy	−10𝑦2𝑥
𝑥𝑦2𝑧		+xy	+𝑥𝑦2	+3
16𝑥𝑦2𝑧	+14xz	+4xy	−9𝑥𝑦2	+3

Thus, (15𝑥𝑦²𝑧 + 14𝑥𝑧 + 3𝑥𝑦 − 10𝑦²𝑥) + (3 + 𝑥𝑦²𝑧 + 𝑥𝑦² + 𝑥𝑦) = 16𝑥𝑦²𝑧 − 9𝑥𝑦² + 4𝑥𝑦 + 14𝑥𝑧 + 3