Question

Factorise: 16x² + 40xy + 25y² - 1 [Answer: (4x + 5y + 1) (4x + 5y - 1) For reference]

Answer 1

Step-by-step explanation:

⇒ 16x² + 40xy + 25y² - 1

⇒ 4²x² + 2*4x*5y + 5²y² - 1

⇒ (4x)² + 2(4x*5y) + (5y)² - 1

Using, a² + 2ab    + b² = (a + b)²

    (4x)² + 2(4x*5y) + (5y)² = (4x + 5y)²

⇒ (4x + 5y)² - 1

⇒ (4x + 5y)² - 1²         {1 = 1²}

Using a² - b² = (a + b)(a - b)

⇒ (4x + 5y + 1)(4x + 5y - 1)

Answer 2

$\implies\sf 16x^2+40xy+25y^2-1 \\ \\ \\ :\implies\sf [(4x)^2+2.4x.5y+(5y)^2]-1\\ \\ \\ \scriptsize{\underline{\sf\bigstar \ \ \ (a+b)^2=a^2+2ab+b^2\ \ }}\\ \\ \\ :\implies\sf (4x+5y)^2-1\\ \\ \\ \scriptsize{\underline{\sf\bigstar \ \ \ a^2-b^2= (a+b)(a-b)\ \ }}\\ \\ \\ :\implies\sf (4x+5y)^2-(1)^2\\ \\ \\ :\implies\sf (4x+5y+1)(4x+5y-1)$

$\underline{\boxed{\mathfrak{ \dag (4x+5y+1)(4x+5y-1)}}}$