# Determine if a Polynomial -2r^3(3r^2-4r-3)

-2r3(3r2-4r-3)
A polynomial is a combination of terms separated using + or – signs. Polynomials cannot contain any of the following:
1. Variables raised to a negative or fractional exponent. (2x-2,x12,…).
2. Variables in the denominator. (1x,1×2,…).
3. Variables under a radical. (x,x3,…).
4. Special features. (trig functions, absolute values, logarithms, …).
Simplify the expression.
Apply the distributive property.
-2r3(3r2)-2r3(-4r)-2r3⋅-3
Simplify.
Rewrite using the commutative property of multiplication.
-2⋅3(r3r2)-2r3(-4r)-2r3⋅-3
Rewrite using the commutative property of multiplication.
-2⋅3(r3r2)-2⋅-4(r3r)-2r3⋅-3
Multiply -3 by -2.
-2⋅3(r3r2)-2⋅-4(r3r)+6r3
-2⋅3(r3r2)-2⋅-4(r3r)+6r3
Simplify each term.
Multiply r3 by r2 by adding the exponents.
Use the power rule aman=am+n to combine exponents.
-2⋅3r3+2-2⋅-4(r3r)+6r3
Add 3 and 2.
-2⋅3r5-2⋅-4(r3r)+6r3
-2⋅3r5-2⋅-4(r3r)+6r3
Multiply -2 by 3.
-6r5-2⋅-4(r3r)+6r3
Multiply r3 by r by adding the exponents.
Multiply r3 by r.
Raise r to the power of 1.
-6r5-2⋅-4(r3r1)+6r3
Use the power rule aman=am+n to combine exponents.
-6r5-2⋅-4r3+1+6r3
-6r5-2⋅-4r3+1+6r3
Add 3 and 1.
-6r5-2⋅-4r4+6r3
-6r5-2⋅-4r4+6r3
Multiply -2 by -4.
-6r5+8r4+6r3
-6r5+8r4+6r3
-6r5+8r4+6r3
Determine if the expression breaks any of the rules.
Does not break any of the rules
Determine if the expression is a polynomial.
Polynomial
Determine if a Polynomial -2r^3(3r^2-4r-3)

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