Asked by kabral
when are the sum.deference,product and quotient of two monomials also a monomial?
Answers
Answered by
oobleck
a monomial has just one term, such as x^2, 3, or 3y
So, if A and B are monomials,
the product is always another monomial
the sum or difference A+B or A-B is also a monomial as long as A and B are both in the same variable and same power. That is, 2x+2x = 4x and 6y-2y = 4y, but 2x+3z is a binomial, since the x and z terms cannot be combined. And 4x^2+5x is also a binomial, since the powers are not the same.
Division is also more complicated. A/B is a monomial if A and B both involve the same variable, and the power of A is not less than the power of B. 6x^3/2x = 3x^2 which is a monomial (as long as x ≠ 0, because division by zero is undefined).
6x/2x^2 = 3/x which is also not a monomial, since polynomials and monomials involve non-negative powers of the variable.
read the article in wikipedia on moomials
So, if A and B are monomials,
the product is always another monomial
the sum or difference A+B or A-B is also a monomial as long as A and B are both in the same variable and same power. That is, 2x+2x = 4x and 6y-2y = 4y, but 2x+3z is a binomial, since the x and z terms cannot be combined. And 4x^2+5x is also a binomial, since the powers are not the same.
Division is also more complicated. A/B is a monomial if A and B both involve the same variable, and the power of A is not less than the power of B. 6x^3/2x = 3x^2 which is a monomial (as long as x ≠ 0, because division by zero is undefined).
6x/2x^2 = 3/x which is also not a monomial, since polynomials and monomials involve non-negative powers of the variable.
read the article in wikipedia on moomials
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