Final answer:
To simplify the expression 3x(4r-5)+3, distribute the 3x and simplify. Then substitute the given values of x into the expression. For the expression a(a²+a+1)+5, simplify by expanding the brackets. Then substitute the given values of a into the expression.
Step-by-step explanation:
To simplify the expression 3x(4r-5)+3, we can distribute the 3x to each term inside the parentheses:
3x(4r-5)+3 = 12xr - 15x + 3
To find the value of the expression when x = 3, we substitute x with 3 in the simplified expression:
12xr - 15x + 3 = 12(3)r - 15(3) + 3 = 36r - 45 + 3 = 36r - 42
To find the value of the expression when x = -2, we substitute x with -2 in the simplified expression:
12xr - 15x + 3 = 12(-2)r - 15(-2) + 3 = -24r + 30 + 3 = -24r + 33
To find the value of the expression when x = 0, we substitute x with 0 in the simplified expression:
12xr - 15x + 3 = 12(0)r - 15(0) + 3 = 0
For the expression a(a²+a+1)+5:
a(a²+a+1)+5 simplifies to a³ + a² + a + 5
To find the value of the expression when a = 0:
a³ + a² + a + 5 = 0³ + 0² + 0 + 5 = 5
To find the value of the expression when a = -1:
a³ + a² + a + 5 = (-1)³ + (-1)² + (-1) + 5 = -1 + 1 - 1 + 5 = 4