An identity is true for all values of its variables. Is the given statement true or false

Solution:

True.

Consider the standard identity, (x + a) (x + b) = x²+ (a + b) x + ab

The above equation is true for all possible values of x, a and b, so it is called an identity.

Let us substitute x = 5, a = 2 and b = -1 and verify the equation

We have, LHS = (x + a) (x + b)

= (5 + 2) (5 - 1)

= 7 × 4 = 28

RHS = x²+ (a + b) x + ab

= (5)² + (2 - 1)5 + (2)(-1)

= 25 + 5 - 2

= 30 - 2 = 28

∴ LHS = RHS

✦ Try This: Verify the identity (a + b)² = a² + 2ab + b² , if a = 3 and b = 4

Given standard identity: (a + b)² = a² + 2ab + b²

Substituting a = 3 and b = 4,

LHS = (a + b)² = (3 + 4)² = (7)² = 49

RHS = a² + 2ab + b² = 3² + (2)(3)(4) + 4² = 9 + 24 + 16 = 49

∴ LHS = RHS

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 9

NCERT Exemplar Class 8 Maths Chapter 7 Sample Problem 7

Summary:

The statement ‘An identity is true for all values of its variables’ is true

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