Subtraction of polynomials – Example

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Subtract (𝟐𝟑𝒂 + 𝒃 − 𝟕𝒃𝒂^𝟑 − 𝟒)𝒇𝒓𝒐𝒎(𝒂𝒃^𝟑 − 𝒃 + 𝟖𝒂 − 𝟏𝟕𝒂^𝟑𝒃) using the column method.

Solution:

Expressing (𝟐𝟑𝒂 + 𝒃 − 𝟕𝒃𝒂^𝟑 − 𝟒) − (𝒂𝒃^𝟑 − 𝒃 + 𝟖𝒂 − 𝟏𝟕𝒂^𝟑𝒃) in the column method,

𝑎𝑏3	-b	+8a	−17𝑎3𝑏
	+b	+23a	−7𝑏𝑎3	-4

In the above arrangement, there is no term under 𝑎𝑏³ as there is no term in the second expression with the same variables. Also, 17𝑎³𝑏 and 7𝑏𝑎³ have the same variables with the same exponents. Hence they are like terms.

As this is subtraction, changing the signs in the second expression to solve,

𝑎𝑏³-b+8a−17𝑎³𝑏

-b-23a+7𝑏𝑎³+ 4

————————–

𝑎𝑏³-2b-15a−10𝑎³𝑏+4

Arranging the terms in the descending order of their exponents,−10𝑎³𝑏 + 𝑎𝑏³ − 15𝑎 − 2𝑏 + 4.

Thus, (𝑎𝑏³ − 𝑏 + 8𝑎 − 17𝑎³𝑏) − (23𝑎 + 𝑏 − 7𝑏𝑎³ − 4) = −10𝑎³𝑏 + 𝑎𝑏³ − 15𝑎 − 2𝑏 + 4.