Question

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

(7) 7 (m² + 5) = 35 + 7m²

Answer 1

7 (m² + 5) = 35 + 7m²
Substitute m = 0
LHS = 7 (m² + 5)
= 7 (0² + 5)
= 7 (0 + 5)
= 7 (5)
= 35
RHS : 35 + 7m²
= 35 + 7 (0)²
= 35 + 0
= 35
∴ LHS = RHS for m = 0
Substitute m = 1
LHS : 7 (m² + 5)
= 7 (1² + 5)
= 7 (1 + 5)
= 7 (6)
= 42
RHS : 35 + 7m²
= 35 + 7 (1)²
= 35 + 7
= 42
∴ LHS = RHS for m = 1
Substitute m = 2
LHS : 7 (m² + 5)
= 7 (2² + 5)
= 7 (4 + 5)
= 7 (9)
= 63
RHS : 35 + 7m²
= 35 + 7 (2)²
= 35 + 28
= 63
∴ LHS = RHS for m = 2
Substitute m = 3
LHS :7 (m² + 5)
= 7 (3² + 5)
= 7 (9+ 5)
= 7 (14)
= 98
RHS : 35 + 7m²
= 35 + 7 (3)²
= 35 + 63
= 98
∴ LHS = RHS for m = 3
As LHS = RHS for all values of m,
7 (m² + 5) = 35 + 7m² is an identity.