Question

Factorise 16x square - 25y square ​

Answer 1

Answer:

(4x-5y)(4x+5y)

Step-by-step explanation:Rewrite  16$x^{2}$ as (4$x^{2}$ )

(4$x^{2}$)-(25$y^{2}$)

Rewrite 25$y^{2}$ as (5$y^{2}$)

(4$x^{2}$)-(5$y^{2}$)

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2}$-$b^{2}$= (a-b)(a+b) where a=4x,b=5x

(4x-5y)(4x+5y)

Answer 2

Given :-

• 16x² - 25y²

Solution :-

Apply identity a² - b² = (a + b)(a - b)

→ 16x² - 25y²

→ (4x)² - (5y)²

→ (4x + 5y)(4x - 5y)

Some Identities :-

• (a + b)² = a² + b² + 2ab
• (a - b)² = a² + b² - 2ab
• (a + b)³ = a³ + b³ + 3ab(a + b)
• (a - b)³ = a³ - b³ - 3ab(a - b)
• a³ - b³ = (a - b)(a² + ab + b²)
• a³ + b³ = (a + b)(a² - ab + b²)