Question

Factorise the following using suitable identity : (i) 25x^(2)+30x+9 (ii) (x^(2)-2xy+y^(2))-z^(2) (iii ) 9x^(2)y^(2)-16 (iv) 4y^(2)-12y+9

Answer 1

The expressions given are factorised using identities that recognize patterns in the coefficients, which result in two perfect square trinomials and two differences of squares.

Step-by-step explanation:

The question asks to factorise quadratics and a difference of squares using suitable identities. Below are the factorisations for the given expressions:

1. 25x² + 30x + 9: This is a perfect square trinomial, which factorises to (5x + 3)².
2. (x² - 2xy + y²) - z²: This is a difference of squares, which factorises to ((x - y) + z)((x - y) - z).
3. 9x²y² - 16: This is also a difference of squares, factorised as (3xy + 4)(3xy - 4).
4. 4y² - 12y + 9: Another perfect square trinomial, factorising to (2y - 3)².

Remember that factoring requires you to look for patterns and apply identities such as the difference of squares and perfect square trinomials.