Basic Mathematics for College Students

Subtract polynomials.

To subtract one monomial from another, we add the opposite of the monomial that is
to be subtracted. In symbols,xyx(y).

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Appendix II Polynomials A-11

EXAMPLE (^6) Subtract: 8x^2  3 x^2
StrategyWe will add the opposite of 3x^2 to 8x^2.
WHYTo subtract monomials, we add the oppostie of the monomial that is to be
subtracted.
Solution
Add the opposite of 3x^2.
Add the coefficients and keep the same variable and
exponent. Think: [8(3)]x^2  5 x^2
 5 x^2
8 x^2  3 x^2  8 x^2  1  3 x^22
Self Check 6
Subtract: 6y^3  9 y^3
Now TryProblem 47
Recall from Chapter 1 that we can use the distributive property to find the
opposite of several terms enclosed within parentheses. For example, we consider
(2a^2 a9).
Replace the symbol in front
of the parentheses with 1.
Use the distributive property
to remove parentheses.
This example illustrates the following method of subtracting polynomials.
Subtracting Polynomials
To subtract two polynomials, change the signs of the terms of the polynomial
being subtracted, drop the parentheses, and combine like terms.
  2 a^2 a 9
(2a^2 a9) 1 (2a^2 a9)
EXAMPLE (^7) Subtract: (3x4.2) (5x7.2)
StrategyWe will change the signs of the terms of 5x7.2, drop the parentheses,
and combine like terms.
WHYThis is the method for subtracting two polynomials.
Solution
Change the signs of each term of 5x7.2
and drop the parentheses.
Combine like terms: Think: (35)x 2 x
and (4.27.2)11.4.
  2 x11.4
 3 x4.2 5 x7.2
(3x4.2 )( 5 x7.2)
Self Check 7
Subtract:
(3.3a5) (7.8a2)
Now TryProblem 51
The binomials in Example 7 can be subtracted by writing them so that like terms
are in columns.
¡ Change signs and add, column by column.
3 x 4.2
 5 x 7.2
 2 x11.4
3 x4.2
^15 x7.2^2