中等MATH-ALGE-006
Which of the following is an identity?
A. x^2 − 1 = (x − 1)^2
B. x^2 − 1 = (x − 1)(x + 1)✓ 答案
C. (x + 1)^2 = x^2 + 1
D. x^2 + 4 = (x + 2)^2
解說
Difference of squares is an identity: (x − 1)(x + 1) = x^2 − 1 for every x. (x − 1)^2 = x^2 − 2x + 1, and (x + 2)^2 = x^2 + 4x + 4, so the other statements fail for most values of x.