Factorize the following. x 2 + 1 x 2 + 2 - 3 x - 3 x

Given, x 2 + 1 x 2 + 2 - 3 x - 3 x Rewriting the given expression, we get: ⇒ x 2 + 2 + 1 x 2 - 3 x + 1 x Now, using identity, we get: ⇒ x + 1 x 2 - 3 x + 1 x ⇒ x + 1 x x + 1 x - 3 Hence, we get the factors as x + 1 x x + 1 x - 3 .

Verify: 3 p 7 + 7 6 p 2 - 3 7 p - 7 6 p 2 = 2

Given, 3 p 7 + 7 6 p 2 - 3 7 p - 7 6 p 2 = 2 Using identity on LHS, we get: ⇒ 3 p 7 + 7 6 p + 3 7 p - 7 6 p 3 p 7 + 7 6 p - 3 7 p - 7 6 p ⇒ 6 p 7 3 p 7 + 7 6 p - 3 7 p + 7 6 p ⇒ 6 p 7 14 6 p ⇒ 14 7 ⇒ 2 In RHS, we have: 2 Therefore, we get: LHS = RHS Hence, verified.