Question

The identity a squared minus B squared equals parentheses a plus B parentheses parentheses a minus B parentheses is true for all values of ANB. Compute the whole number value of 2021 squared -2022The identity a squared minus B squared equals parentheses a plus B parentheses parentheses a minus B parentheses is true for all values of A and B. Compute the whole number value of 2021 squared -2020 squared

Answer 1

Question:

The identity
`A^2 - B^2 = (A + B) (A - B)` is true for all values of A and B. Compute the whole number value of
`2021^2 -2022^2`

Answer:

`2021^2 - 2022^2 = -4043`

Explanation:

Given

`A^2 - B^2 = (A + B) (A - B)`

Required

Solve:
`2021^2 -2022^2`

In:
`2021^2 -2022^2`

`A = 2021; B = 2022`

`A^2 - B^2 = (A + B) (A - B)` becomes

`2021^2 - 2022^2 = (2021 + 2022)(2021 - 2022)`

`2021^2 - 2022^2 = (4043)(-1)`

`2021^2 - 2022^2 = -4043`