Adding and Subtacting Polynomials with Different Variables
Read this topicExplanations 3
- Adding and Subtracting Polynomials One of the first things we learn is addition of integers. At this point in your math career, if I asked "What is 1+21+21+2?", you would be abl…
By Tommy San Miguel, Catherine Yeo, Alex Federspiel, Zora Gilbert, Jonathan Heller
- (Video) Add and Subtract Polynomials with Several Variables by Alane Tetoni The video by Alane Tetoni shows how to add and subtract polynomials with multiple variables. Summary\…
By Stefan Cuevas, Alex Federspiel, Amy Feraco, Jonathan Heller, Caroline K
- Adding or Subtracting Polynomials with Multiple Variables When adding or subtracting polynomials, remember these three steps: Step One: Distribute (if subtracting) because of th…
By Hannah Bonville, Naomi Burgess, Alex Federspiel, Jonathan Heller, Caroline K
Problems 23
- Simplify the following expression: (9x2−3y+z3)−(17y+12z3−2x2)(9x^2-3y+z^3) - (17y+12z^3-2x^2)(9x2−3y+z3)−(17y+12z3−2x2)
- What is the sum of the following two polynomials? 3x2y−5xy23x^2y - 5xy^23x2y−5xy2 7xy2−4x2y7xy^2 - 4x^2y7xy2−4x2y
- What is the sum of the following polynomials? 2x2−2y2+3z2−4x2y+xyz2x^2 - 2y^2 + 3z^2 - 4x^2y + xyz2x2−2y2+3z2−4x2y+xyz 2y2+3z2−4xy2+z2y^2 + 3z^2 - 4xy^2 + z2y2+3z2−4xy2+z
- Simplify the following expression. (10x2−4y+z3)−(108y+15z3−4x2)(10x^2-4y+z^3) - (108y+15z^3-4x^2)(10x2−4y+z3)−(108y+15z3−4x2)
- Which of the following expressions are equal to x2yz3+x2y3x^2yz^3 + x^2y^3x2yz3+x2y3?
- Consider the two polynomials V=(xyz+x2y)V = (xyz + x^2y)V=(xyz+x2y) and U=(2xyz+x2y+xy)U = (2xyz + x^2y + xy)U=(2xyz+x2y+xy). \\ What is V+UV+UV+U?
- Simplify 7x−[2(x2−3z)+4(x2+y)−7z]+8z2.7x-[2(x^2-3z)+4(x^2+y)-7z]+8z^2.7x−[2(x2−3z)+4(x2+y)−7z]+8z2.
- Simplify (107x5+80y4+50x3−21y2)+(51x5+70y4+32x3+7y2)\left(107x^5+80y^4+50x^3-21y^2\right)+\left(51x^5+70y^4+32x^3+7y^2\right)(107x5+80y4+50x3−21y2)+(51x5+70y4+32x3+7y2).
- Simplify (2xy2−3x2y)+(xy2+4x2y)(2xy^2 - 3x^2y) + (xy^2 + 4x^2y)(2xy2−3x2y)+(xy2+4x2y).
- Which terms in the expression 5a+3a2−5b+2b25a + 3a^2 - 5b + 2b^25a+3a2−5b+2b2 can be combined?
- Which of the following are like terms?
- How many terms will the following expression have when simplified? (2x2+3xy−2z)+(4x2−2yz+5xy)(2x^2 + 3xy - 2z) + (4x^2 - 2yz + 5xy)(2x2+3xy−2z)+(4x2−2yz+5xy)
- Michelle is trying to simplify the following expression: (8ab+2ac−b)+(3ac+b2+2a)(8ab + 2ac - b) + (3ac + b^2 + 2a)(8ab+2ac−b)+(3ac+b2+2a) Which terms can she combine?
- What are the degrees of these polynomials, respectively? 2x2+3xy−42x^2 + 3xy - 42x2+3xy−4 4xy2−2y2+3y4xy^2 - 2y^2 + 3y4xy2−2y2+3y
- Find the sum. (2ab−b2c+ac2−abc)−(4b2c−3ac2+abc)(2ab - b^2c + ac^2 - abc) - (4b^2c - 3ac^2 + abc)(2ab−b2c+ac2−abc)−(4b2c−3ac2+abc)?
- What is the name of this expression when simplified? (xyz−x2y)+(yz−xyz)(xyz - x^2y) + (yz - xyz)(xyz−x2y)+(yz−xyz)
- What are the like terms in 3x2−2xy+xy2−4x2y+5xy+3y23x^2 - 2xy + xy^2 - 4x^2y + 5xy + 3y^23x2−2xy+xy2−4x2y+5xy+3y2?
- If Gus has 2x−3y2x - 3y2x−3y strips of bacon, how many strips of bacon does Holly need in order for there to be 4x+7y4x + 7y4x+7y strips of bacon total?
- Which of the following is equivalent to this equation: 4x3y2−x2y=5x3y24x^3y^2 - x^2y = 5x^3y^24x3y2−x2y=5x3y2
- Simplify 9x2y4−xy2\sqrt{9x^2y^4} - xy^29x2y4−xy2 if x,y>0x,y>0x,y>0.
- Which of the following are multivariable polynomials?
- Add the following polynomials: (6x2y+5y2x+7x−2y−19)+(3y2x+5x2y+2y−9x+8)(6x^{2}y+5y^{2}x+7x-2y-19)+(3y^{2}x+5x^{2}y+2y-9x+8)(6x2y+5y2x+7x−2y−19)+(3y2x+5x2y+2y−9x+8)
- Evaluate the following expression: (3y3x+7x2−9xy+14)−(8y3x+6x2+3x−8xy−11)(3y^{3}x+7x^{2}-9xy+14)-(8y^{3}x+6x^{2}+3x-8xy-11)(3y3x+7x2−9xy+14)−(8y3x+6x2+3x−8xy−11)