Polynomials
x4y5
x3y6
Do you mean
(x^4 y^5) / (x^3 y^6) ??????
If so, remember when you divide you subtract exponents.
=x^(4-3) y^ (5-6)
=x^1 y^-1
which is
= x/y
These expressions you have written are polynomials. A polynomial is an algebraic expression consisting of variables, coefficients, and exponents, combined using addition, subtraction, and multiplication. Each term in a polynomial consists of a variable raised to a non-negative integer exponent, multiplied by a coefficient.
Let's break down the two given polynomials:
1. x^4y^5:
- This polynomial has two terms: x^4 and y^5.
- In the first term, x is raised to the power of 4, while in the second term, y is raised to the power of 5.
- Both terms have implicit coefficients of 1, meaning that the coefficients are 1 by default.
- The overall polynomial is the sum of these two terms.
2. x^3y^6:
- Similarly, this polynomial also has two terms: x^3 and y^6.
- In the first term, x is raised to the power of 3, while in the second term, y is raised to the power of 6.
- Again, both terms have implicit coefficients of 1.
- Like the previous polynomial, this one is also the sum of the two terms.
These polynomials can be simplified by combining like terms. In this case, you cannot combine the terms since they have different variables and exponents. However, if you want to add or subtract the polynomials, you can simply add or subtract the coefficients of the like terms.
For example, if you wanted to add x^4y^5 and x^3y^6, you would combine the coefficients of the like terms (which are both 1):
x^4y^5 + x^3y^6 = 1x^4y^5 + 1x^3y^6 = (1 + 1)x^4y^5 + x^3y^6 = 2x^4y^5 + x^3y^6
If you have any further questions about polynomials or need any additional explanations, feel free to ask!