Question

Simplify the following expressions and evaluate them as directed:

x² (3−2x+x² ) for x=1; x=−1; x=2/3 and x=−1/2

Answer 1

To simplify the expression x²(3−2x+x²) for different values of x, substitute the given values of x into the expression and simplify.

Step-by-step explanation:

To simplify the expression and evaluate it for different values of x, we can substitute the given values of x into the expression and simplify.

For x = 1:

x²(3−2x+x²) = 1²(3−2(1)+1²) = 1(3−2+1) = 1(2) = 2

For x = -1:

x²(3−2x+x²) = (-1)²(3−2(-1)+(-1)²) = 1(3+2+1) = 1(6) = 6

For x = 2/3:

x²(3−2x+x²) = (2/3)²(3−2(2/3)+(2/3)²) = (4/9)(3−(4/3)+(4/9)) = (4/9)(3−(12/9)+(4/9)) = (4/9)(3−(12+4)/9) = (4/9)(3−16/9) = (4/9)(-13/9) = -52/81

For x = -1/2:

x²(3−2x+x²) = (-1/2)²(3−2(-1/2)+(-1/2)²) = (1/4)(3+1+1/4) = (1/4)(15/4) = 15/16