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Which property of polynomial multiplication says that the product of two polynomials is always a polynomial?
That property is called CLOSURE.
What property of polynomial multiplication says that the product of two polynomials is always a polynomial?
Clouser
Do you use the distributive property with a monomial and a polynomial?
If you want to multiply the monomial by the polynomial, yes. In that case, you have to multiply the monomial by every term of the polynomial. For example: a (b + c + d) = ab + ac + ad More generally, when you multiply together two polynomials, you have to multiply each term in one polynomial by each term of the other polynomial; for example: (a + b)(c + d) = ac + ad + bc + bd All this can be derived from the distributive property (just apply the distributive property repeatedly).
Can multiplication be distributive over subtraction?
Multiplication can be the first step when using the distributive property with subtraction. The distributive law of multiplication over subtraction is that the difference of the subtraction problem and then multiply, or multiply each individual products and then find the difference.
Is subtraction an identity property?
Subtraction is not an identity property but it does have an identity property. The identity is 0 and each number is its own inverse with respect to subtraction. However, this is effectively the same as the inverse property of addition so there is no real need to define it as a separate property.
