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# Subtracting Polynomials

When we subtract polynomials, we subtract the like terms. Because a - b = a + (-b), we can subtract by adding the opposite of the second polynomial to the first polynomial. Remember that a negative sign in fron of parentheses changes the sign of each term in the parentheses. For example,

-(x2 - 2x + 8) = -x2 + 2x - 8.

Polynomials can be subtracted horizontally or vertically, as shown in the next example.

Subtracting polynomials

Perform the indicated operation.

a) (x2 - 5x - 3) - (4x2 + 8x - 9)

b) (4y3 - 3y + 2) - (5y2 -7y - 6)

Solution

 a) (x2 - 5x - 3) - (4x2 + 8x - 9) = x2 - 5x - 3 - 4x2 - 8x + 9 Change signs. = -3x2 - 13x + 6 Add.

b) To subtract 5y2 - 7y -6 from 4y3 - 3y + 2 vertically, we line up the like terms as we do for addition:

 4y3 - 3y + 2 - (5y2 - 7y - 6)

Now change the signs of 5y2 - 7y - 6 and add the like terms:

 4y3 - 3y + 2 -5y2 + 7y + 6) 4y3 -5y2 + 4y + 8

Caution

when adding or subtracting polynomials vertically, be sure to line up the like terms.