Question

resolve the following into factories : 49-x^2-y^2+2xy​

Answer 1

Required Answer:-

Given to Factorise:

• 49 - x² - y² + 2xy

Solution:

We have,

= 49 - x² - y² + 2xy

This can be written as,

= 49 - [x² - 2xy + y²]

As (x - y)² = x² - 2xy + y². So,

49 - [x² - 2xy + y²]

= 49 - (x - y)²

= 7² - (x - y)²

As a² - b² = (a + b)(a - b), factorise,

= (7 + x - y)(7 - x + y)

Hence, the factorised form is (x + 7 - y)(y + 7 - x)

Answer:

• The factorised form of the polynomial is (x + 7 - y)(y + 7 - x)

Identity Used:

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