Question

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

(3) x (x + 2) = x² + 2x

Answer 1

x (x + 2) = x² + 2x
Substitute x = 0
LHS : x (x + 2)
= 0 (0 + 2)
= 0 (2)
= 0
RHS : x² + 2x
= (0)² + 2 (0)
= 0 + 0
= 0
∴ LHS = RHS for x = 0
Substitute x = 1
LHS : x (x + 2)
= 1 (1 + 2)
= 1 (3)
= 3
RHS : x² + 2x
= (1)² + 2 (1)
= 1 + 2
= 3
∴ LHS = RHS for x = 1
Substitute x = 2
LHS : x (x + 2)
= 2 (2 + 2)
= 2 (4)
= 8
RHS : x² + 2x
= (2)² + 2 (2)
= 4 + 4
= 8
∴ LHS = RHS for x = 2
Substitute x = 3
LHS : x (x + 2)
= 3 (3 + 2)
= 3 (5)
= 15
RHS : x² + 2x
= (3)² + 2 (3)
= 9 + 6
= 15
∴ LHS = RHS for x = 3
As LHS = RHS for all values of x,
x (x + 2) = x² + 2x is an identity.