Answer to Question #449 in Algebra for jacob

Question

How is it possible to overwrite the expressions without using the modulus sign:

a) |a²|;
b) |a − b|, if a > b;
c) |a − b|, if a < b;
d) | − a|, if a is negative?

Answer 1

a) Since a² cannot be negative, its absolute value is also a². Thus, |a²| = a²;
b) Since a > b, |a − b| = (a − b);
c) Since a < b, |a − b| = (b − a);
d) Since a < 0, | − a| = −a.