# Determine if a Polynomial -4/3*(y-15)-1/9y

-43⋅(y-15)-19y
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.
Simplify each term.
Apply the distributive property.
-43y-43⋅-15-19y
Combine y and 43.
-y⋅43-43⋅-15-19y
Cancel the common factor of 3.
Move the leading negative in -43 into the numerator.
-y⋅43+-43⋅-15-19y
Factor 3 out of -15.
-y⋅43+-43⋅(3(-5))-19y
Cancel the common factor.
-y⋅43+-43⋅(3⋅-5)-19y
Rewrite the expression.
-y⋅43-4⋅-5-19y
-y⋅43-4⋅-5-19y
Multiply -4 by -5.
-y⋅43+20-19y
Move 4 to the left of y.
-4y3+20-19y
Combine y and 19.
-4y3+20-y9
-4y3+20-y9
To write -4y3 as a fraction with a common denominator, multiply by 33.
-4y3⋅33-y9+20
Write each expression with a common denominator of 9, by multiplying each by an appropriate factor of 1.
Multiply 4y3 and 33.
-4y⋅33⋅3-y9+20
Multiply 3 by 3.
-4y⋅39-y9+20
-4y⋅39-y9+20
Combine the numerators over the common denominator.
-4y⋅3-y9+20
Simplify each term.
Simplify the numerator.
Factor y out of -4y⋅3-y.
Factor y out of -4y⋅3.
y(-4⋅3)-y9+20
Factor y out of -y.
y(-4⋅3)+y⋅-19+20
Factor y out of y(-4⋅3)+y⋅-1.
y(-4⋅3-1)9+20
y(-4⋅3-1)9+20
Multiply -4 by 3.
y(-12-1)9+20
Subtract 1 from -12.
y⋅-139+20
y⋅-139+20
Move -13 to the left of y.
-13⋅y9+20
Move the negative in front of the fraction.
-13y9+20
-13y9+20
-13y9+20
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 -4/3*(y-15)-1/9y