Subtracting Polynomials
To subtract one polynomial from another, add the first polynomial to the
opposite of the polynomial being subtracted.
To find the opposite of a polynomial, multiply each term by -1.
For example:
The opposite of 5x2 is -5x2.
The opposite of -2x + 7 is 2x - 7.
Note:
Here’s a way to find the opposite of a
polynomial:
Change the sign of each term.
Example 1
Find: (-18w2 + w - 32) - (40 - 13w2)
| Solution
Change the subtraction to
addition of the opposite.
Remove the parentheses.
Write like terms next to
each other.
Combine like terms. |
(-18w2 + w - 32) - (40 - 13w2)
= (-18w2 + w - 32) + (-1)(40 - 13w2)
= -18w2 + w - 32 - 40 + 13w2
= -18w2 + 13w2 + w - 32 - 40
= -5w2 + w - 72 |
So, (-18w2 + w - 32) - (40 - 13w2) = -5w2 +
w - 72
Note:We can also place one polynomial beneath
the other and subtract like terms.
To do the subtraction, we change the sign
of each term being subtracted, then add.
Example 2
Subtract (15z2 - 5yz2 + 4y3) from (6y3
- 10z3 + 2yz2).
Solution
Be careful! “Subtract A from B†means B - A. The order is important.
| Write the difference.
Change the subtraction to
addition of the opposite.
Remove the parentheses.
Write like terms next to
each other.
Combine like terms. |
(6y3
- 10z3 + 2yz2) - (15z2 - 5yz2 + 4y3)
= (6y3
- 10z3 + 2yz2) + (-1) (15z2 - 5yz2 + 4y3)
= 6y3
- 10z3 + 2yz2 - 15z2 + 5yz2
- 4y3
= 6y3 - 4y3
- 10z3 + 2yz2 + 5yz2 - 15z2
= 2y3
- 10z3 + 7yz2 - 15z2 |
Note:
We can also place one polynomial beneath
the other and subtract like terms.
To do the subtraction, we change the sign
of each term being subtracted, then add.
 |
