-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, …).

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)