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### Course: Algebra (all content)>Unit 10

Lesson 3: Adding & subtracting polynomials: two variables

# Subtracting polynomials: two variables (intro)

Sal simplifies (4x²y - 3xy + 25) - (9y²x + 7xy - 20). Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• IS 4x^2y - 10xy - 9y^2x + 45 also acceptable? ...... I just swopped two of the terms around.
• Ideally, you'd write it in order of decreasing powers with the variable first in alphabetical order. Sadly, it gets more complicated with multiple variables and when you have different powers.
Personally, I'd write it like you did: The x's are in order of decreasing power, and the y's highest power is after the one with y^1. Just personal preference really. I would never say it's wrong if you write it in a different order: it's just how you interpret your answer.

Hope I helped!
• Why does he put his answers in that order?
• It is in polynomial standard form which is from highest to lowest exponent value.
(1 vote)
• isn't negative 3 minus seven suppose to be negative 7 because the 7 is followed by a minus sign?
• in my answer i got -5x^2y-10xy+45
i thought that because 4x^2y-9x^2y would equal -5x^2y
but instead he counted them as two different like terms,
why is that?
• saeed, I think you misread. That second term is (-9)y^2x - the y is squared not the x. The terms are not like terms.
• At , why did Sal wrote a number 1 in between of the quantities? What is the purpose of that?
(4x²y - 3xy + 25) - `1` (9y²x + 7xy - 20)
• Just to show that it is a negative one for all number in the parentheses instead of just the first number.
• what if the question is like 9xy - 12yx. what would u do here. would these be considered as LIKE TERMS
• Yes they're like terms and should be simplified. You won't get marked wrong
• How do you write this in standard form for this? Which variable comes first?
• The most common way is seen polynomials arranged is to have the highest power of the lowest letter of the variables go first and then arrange the remaining items in a "descending" order where the constant is the last item in the arrangement. You don't have to arrange it on any particular order. We can arrange them however we want due to the commutativity of addition. What really matters is that you can tell the difference between the terms and understand that objects like (x^2)(y) and (x)(y^2) are not necessarily the same thing. Hope this helps. Good luck!
• if you add x and x together does that make x^2
(1 vote)
• When you add two like terms, you always combine the co-factors. x + x would produce 2x rather than x^2. However, x*x will produce x^2
(1 vote)
• I am confused. Like what would be the answer if you did x to the fourth power plus x to the 3rd power
• You would be left with x^4 + x^3. You are unable to add different powers of the same variable. The order of operations states that exponents must be evaluated before addition, but since the exponent cannot be evaluated without knowing the value of x, the addition cannot be done either.
(1 vote)
• please explain how to work out the following 1/3 (3a + 2) + 1/4 (4a-2)
• 1st change 4a-2 to 4a+ (-2)
1/3 (3a + 2) + 1/4 (4a + (-2))
Then distribute 1/3.
1/3*3a + 1/3*2 + 1/4 (4a + (-2))
Simplify.
a + 2/3 + 1/4 (4a + (-2))
Then distribute 1/4.
a + 2/3 + 1/4*4a + 1/4*(-2)
Simplify
a + 2/3 + a + (-2/4)
Combine like terms: a + a & 2/3 + (-2/4)
Fractions must have common denominators to find the sum, 2/3 =4/6 & -2/4 = -3/6, therefore 4/6 + (-3/6) = 1/6.
2a +1/6