Statement 1: The product of two binomials is a trinomial, conversely if we factorise a trinomial we always obtain two binomial factors

Statement 2: The square of the difference of two terms = the sum of the same two terms x their difference.

Which of the following options is correct?

1. Both the statements are true.

2. Both the statements are false.

3. Statement 1 is true, and statement 2 is false.

4. Statement 1 is false, and statement 2 is true.

The product of two binomials is a trinomial.

For example; (x + 2)(x + 3) = x(x + 3) + 2(x + 3)

= x² + 3x + 2x + 6

= x² + 5x + 6

Here, (x + 2) and (x + 3) are two binomials and their product x² + 5x + 6 is a trinomial.

But, (x + 2)(x - 2) = x² - 2²

= x² - 4

Here, (x + 2) and (x - 2) are two binomials but x² - 4 is not a trinomial.

So, we can say that the product of two binomials is not always a trinomial.

Conversely, if we factorize a trinomial, we always obtain two binomial factors.

This is not always true:

Some trinomials cannot be factorized into binomials with real coefficients.

So, statement 1 is false.

The square of the difference of two terms = the sum of the same two terms × their difference.

L.H.S. = (a - b)²

= a^{2+ 2ab - b2}

R.H.S. = (a + b) x (a - b)

= a^{2- b2}

As, L.H.S. ≠ R.H.S.

So, statement 2 is false.

Hence, option 2 is the correct option.