Question

Identify the identities from the following by replacing the variables with the values 0, 1, 2 and 3.

(4) p (p − 4) = p² − 4p

Answer 1

p (p − 4) = p² − 4p
Substitute p = 0
LHS: p (p − 4)
= 0 (0 − 4)
= 0 (−4)
= 0
RHS : p² − 4p
= (0)² − 4 (0)
= 0 - 0
= 0
∴ LHS = RHS for p = 0
Substitute p = 1
LHS : p (p − 4)
= 1 (1 − 4)
= 1 (− 3)
= − 3
RHS : p² − 4p
= (1)² − 4 (1)
= 1 − 4
= − 3
∴ LHS = RHS for p = 1
Substitute p = 2
LHS : p (p − 4)
= 2 (2 − 4)
= 2 (− 2)
= − 4
RHS : p² − 4p
= (2)² − 4 (2)
= 4 − 8
= − 4
∴ LHS = RHS for p = 2
Substitute p = 3
LHS : p (p − 4)
= 3 (3 − 4)
= 3 (− 1)
= − 3
RHS : p² − 4p
= (3)² − 4 (3)
= 9 − 12
= − 3
∴ LHS = RHS for p = 3
As, LHS = RHS for all values of p,
p (p − 4) = p² − 4p is an identity.