Subtracting Polynomials
Subtracting polynomials is very similar to adding them, but there is one step that you have to do first. Before you combine like terms, you must distribute the negative sign. Here's how this works: (x^{2}+3x-8)-(4x^{2}+5x-7) Notice that there is a negative sign in front of the second trinomial. This means that you need to change the sign of every term in the second trinomial. We do not change the signs on the first trinomial because there is no negative sign in front of it (it is not the one being subtracted). Let's rewrite the polynomial, changing the signs on the 2^{nd} trinomial: x^{2}+3x-8-4x^{2}-5x+7
Take special note how the 4x^{2} was originally positive but is now negative. The negative sign in front of the whole trinomial is now gone because we have distributed it by changing all the signs. Now you're ready to add like terms just like we did with addition. Identify your sets of like terms (let's color them): x^{2}+3x-8-4x^{2}-5x+7. Now add each set of like terms to get your answer: -3x^{2}-2x-1 Examples: 1) (3y^{2}+5y+8)-(2y^{2}-4y+9)= 3y^{2}+5y+8-2y^{2}+4y-9=y^{2}+9y-1
Distribute the negative to each term in the 2nd trinomial by changing the signs: 3y^{2}+5y+8-2y^{2}+4y-9. Now combine the like terms to get your answer: y^{2}+9y-1 2) (6x^{2}+8)-(4x^{2}+x-11)=6x^{2}+8-4x^{2}-x+11=2x^{2}-x+19 Distribute the negative to each term in the 2^{nd} trinomial by changing the signs: 6x^{2}+8-4x^{2}-x+11. Now add like terms: 2x^{2}+19-x. Notice we just wrote the -x term as it was since it didn't have another term to combine with. This answer is not in standard form, so rewrite it in standard form for the final answer: 2x^{2}-x+19 Practice: Subtract the polynomials 1) (6x^{2}+4x-1)-(4x^{2}+7x-8)
2) (9a^{2}-3a+2)-(4a+6)
3) (3x+4y)-(2x+8y)
4) (3y+11)-(y^{2}-3y)
5) (2x^{2}-8x-2)-(2x^{2}+3x+1) Answers: 1) 2x^{2}-3x+7)2) 9a^{2}-7a-4 3) x-4y 4) -y^{2}+6y+11 5) -11x-3 |
Related Links: Math Algebra Factors Polynomials Algebra Topics |