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Question 18384: SUBTRACT POLYNOMIALS
I am having trouble trying to understand these problems please help me.
(3x^2+5x-2)-((7x^2-5x+4)=
((2y^2-y+3)-(y^2-y-4)=
(y^2+y-6)-(y^2+5y-6)=
CAN YOU HELP ME WITH THESE PROBLEMS AND EXPLAIN HOW TO DO THEM?
Answer by smik(40)   (Show Source):
You can put this solution on YOUR website! Let's get right into it. When subtracting terms from a polynomial you can only subtract like terms with the same degree. This is to say that you can't subtract 7x^4 - 7x^2 (because the exponents are not equal), and you can't subtract 3x^4 - 3y^4 (because the variables are different), though you can subtract 9x^4 - 6x^4 (as both the exponents and the variables are the same), which would give us 3x^4.
For the first problem (3x^2+5x-2)-(7x^2-5x+4), we have to foil everything out as we can't subtract them yet due to the fact that they're in brackets. The first part - (3x^2+5x-2) - doesn't change a lot and just becomes: 3x^2+5x-2. However, the second part - "-(7x^2-5x+4)" - has to be foiled out keeping in mind that there's a negative (which you can think of as -1) in front of the whole thing. This foiled out would give us: -7x^2+5x-4.
Hence, the whole expression written without brackets would like the following:
3x^2+5x-2-7x^2+5x-4
And so we go on to add all the like terms:
3x^2-7x^2 = -4x^2
5x+5x = 10x
-2-4 = -6
The subtraction of the two polynomials gives us: -4x^2+10x-6
Now, let's do the second problem together just to get a better grip on things and you can try the third on your own.
(2y^2-y+3)-(y^2-y-4)
First we foil everything out. The first part stays the same, and the second part in brackets is foiled out keeping the negative infront of the brackets in mind. Once everything is foiled out you should get something like this:
2y^2-y+3-y^2+y+4
Now we can add the like terms:
2y^2-y^2 = y^2
-y+y = 0 (the y's cancel out)
3+4 = 7
Therefore our final answer is: y^2+7
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