Let's solve the expression step-by-step:
[tex]\[ 2015^2 - 2015 \times 2014 - 2014^2 + 2014 \times 2015 \][/tex]
First, let's compute each term individually:
1. [tex]\( 2015^2 \)[/tex]:
[tex]\[ 2015^2 = 4060225 \][/tex]
2. [tex]\( 2015 \times 2014 \)[/tex]:
[tex]\[ 2015 \times 2014 = 4058210 \][/tex]
3. [tex]\( 2014^2 \)[/tex]:
[tex]\[ 2014^2 = 4056196 \][/tex]
4. [tex]\( 2014 \times 2015 \)[/tex]:
[tex]\[ 2014 \times 2015 = 4058210 \][/tex]
Now, substitute these values back into the original expression:
[tex]\[ 4060225 - 4058210 - 4056196 + 4058210 \][/tex]
Next, we'll simplify the expression step-by-step:
1. First handle the addition and subtraction involving the smaller terms [tex]\( - 4058210 \)[/tex] and [tex]\( + 4058210 \)[/tex]:
[tex]\[ 4060225 - 4058210 = 2015 \][/tex]
[tex]\[ 2015 - 4056196 = -4054181 \][/tex]
[tex]\[ -4054181 + 4058210 = 4029 \][/tex]
So the final result is:
[tex]\[ 2015^2 - 2015 \times 2014 - 2014^2 + 2014 \times 2015 = 4029 \][/tex]
