Question

Factorize 16-x square -2xy -y square

Answer 1

Answer:

16-x²- 2xy - y²

16- ( x²+ 2xy+ y²)

16 - (x+ y)²

( 4+x+ y)(4-x-y) ( using a²- b² = (a+ b)(a-b)

Answer 2

Answer:

16 - x² - 2xy - y² = (4 + x + y)(4 - x - y)

Step-by-step explanation:

We have,

16 - x² - 2xy - y²

Taking negative common

= 16 - (x² + 2xy + y²)

We know that,

(x + y)² = x² + 2xy + y²

= 16 - (x + y)²

Let's say (x + y) = A

So,

= 16 - (A)²

= 4² - A²

Using the identity,

x² - y² = (x + y)(x - y)

So,

4² - A² = (4 + A)(4 - A)

Now,

we said, A = (x + y)

So,

4² - (x + y)² = (4 + (x + y))(4 - (x + y))

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

Thus,

16 - x² - 2xy - y² = (4 + x + y)(4 - x - y)

Hope it helped and believing you understood it........All the best