Express the following as difference of two squares:

(i) (x + 2z)(2x + z);

(ii) 4(x + 2y)(2x + y);

(iii) (x + 98)(x + 102);

(iv) 505 × 495.

(i) We use

(x + 2z)(2x + z) =

⇒ (x + 2z)(2x + z) =

(ii) 4(x + 2y)(2x + y) = (2x + 4y)(4x + 2y)

We use

⇒ 4(x + 2y)(2x + y) =

⇒ 4(x + 2y)(2x + y) = ( 3x + 3y)²-(2y – 2x)²

(iii) We use

(x + 98)(x + 102) =

⇒ (x + 98)(x + 102) = (x + 100)²-(x-100)²

(iv) 505 × 495 = (500 + 5)(500-5)

We use (a + b)(a - b) = a² - b²

⇒ 505 × 495 = 500²-5²