Question

7. 4- x2 - y2 - 2xy is equal to
(a) (2 - x + y)(2 + x - y)
(c) (2 + x - y)(2 + x + y)
(6)(2 + x + y)(2 - x - y)
(d) (2 - x + y)(2 - x - y)
​

Answer 1

Answer:

(2 + x + y)(2 - x - y)

Step-by-step explanation:

⇒ 4 - x² - y² - 2xy

⇒ 4 - (x² + y² + 2xy)

       Using:  x² + y² + 2xy = (x + y)²

⇒ 2² - (x + y)²

       Using:  a² - b² = (a + b)(a - b)

⇒ (2 + x + y)(2 - (x + y) )

⇒ (2 + x + y)(2 - x - y)

Therefore, 4 - x² - y² - 2xy = (2 + x + y)(2 - x - y).

Answer 2

• Given Relation,

$\longrightarrow \sf 4 - x² - y² - 2xy$

$\longrightarrow \sf 4 - (x² + y² + 2xy)$

• Here we can use identity of ( x² + y² + 2xy ) = (x + y)²
• And also 4 = 2²
• Hence,

$\longrightarrow \sf 2² - (x + y)²$

• Now, again here we have to use another identity of x² - y² = (x - y) (x + y)
• Hence,

$\longrightarrow \sf (2)² - (x +y)²$

$\longrightarrow \sf (2 + (x + y)) (2 - (x + y))$

$\longrightarrow \sf \underline{ \boxed{ \sf (2 + x + y )(2 - x - y )} }$

So, Option (b) is right ✔️

I hope it helps you ❤️✔️