Question

What must be subtracted from a³ − 4a² + 5a − 6 to obtain a² − 2a + 1?

Answer 1

Let the expression to be subtracted be X.
(a³ − 4a² + 5a − 6)-X = (a² − 2a + 1)
X = (a³ − 4a² + 5a − 6)- (a² − 2a + 1)
Since '-' sign precedes the parenthesis, we remove it and change the sign of each term within the parenthesis.
X = a³ − 4a² + 5a − 6- a² + 2a - 1
Rearranging and collecting the like terms:
X = a³ +(− 4-1)a² + (5+2)a − 6 - 1
X = a³ −5a² + 7a − 7
So, a³ −5a² + 7a − 7 must be subtracted from a³ − 4a² + 5a − 6 to obtain a² − 2a + 1.