Question

Please solve the question

Answer 1

Identity:

1. (x + y)² = x² + 2xy + y²
2. (x - y)² = x² - 2xy + y²
3. x² - y² = (x + y)(x - y)

Step-by-step explanation:

a) x² + 2xy + y² - z²

= (x + y)² - z² (Using Identity 1)

= (x + y + z)(x + y - z) (Using Identity 3)

b) 9a² + 12ab + 4b²

= (3a)² + 2(3a)(2b) + (2b)² (Using Identity 1)

= (3a + 2b)²

c) 4p² - 20pq + 25q²

= (2p)² - 2(2p)(5q) + (5q)² (Using Identity 2)

= (2p + 5q)²

d) 1 - 16x² + 64x⁴

= 1 - 2(1)(8x²) + (8x²)² (Using Identity 2)

= (1 - 8x²)²

e) 16x² - 9y²

= (4x)² - (3y)² (Using Identity 3)

= (4x + 3y)(4x - 3y)