Question

Factorise:49-x^2-y^2+2xy

Answer 1

49 - x² - y² + 2xy

7² - (x² + y² - 2xy)

By identity, (a-b)²=a²+b²-2ab

7² - (x - y)²

By identity, a²-b²=(a+b) (a-b)


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


I hope this will help you

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Answer 2

Concept

Factorization or factoring consists of writing variety or another mathematical object as a product of several factors, usually smaller or simpler objects of the identical kind. it's simply the resolution of an integer or polynomial into factors specified when multiplied together they'll end in original or initial the integer or polynomial. within the factorization method, we reduce any algebraic or quadratic into its simpler form, where the equations are represented because the product of things rather than expanding the brackets. The factors of any equation is an integer, a variable or an algebraic expression itself.

Given

49-$x^{2} -y^{2} +2xy$

To find

Factorize: 49-$x^{2} -y^{2} +2xy$.

Explanation

We have to factorize the expression which is completed as under:

49-$x^{2} -y^{2} +2xy$=$7^{2} -(x^{2} +y^{2}-2xy)$

=$7^{2}-(x-y)^{2}$        ($A^{2} -B^{2} = (A+B)(A-B)$

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

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

Hence the factors of 49-$x^{2} -y^{2} +2xy$ are (7+x-y) (7-x+y).

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