Question

what is the answer or full identity of x^{2} -y^{2} =?

Answer 1

Trying to factor as a Difference of Squares:

Factoring:  x²-y²

Theory: A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) × (A-B)

Proof :  (A+B) × (A-B) =

        A2 - AB + BA - B2 =

        A2 - AB + AB - B2 =

        A2 - B2

Note:  AB = BA is the commutative property of multiplication.

Note:  - AB + AB equals zero and is therefore eliminated from the expression.

Check:  x²  is the square of  x¹

Check:  y²  is the square of  y¹

Factorization is :  (x + y)  ×  (x - y)

Answer 2

Answer:

On solving $x^{2} - y^{2}$ using identity we get , $( x + y ) (x - y )$

Step-by-step explanation:

To solve : $x^{2} - y^{2}$ using identity .

Solution :

• We have to solve $x^{2} - y^{2}$ using identity .  
• Algebraic identity is equality which is true for all the values of the variables .  
• We can see that expression is of the form $a^{2}- b^{2} = ( a + b) ( a -b)$
• Here $a = x$ and $b = y$
• Applying the above identity we get solution for  $x^{2} - y^{2}$ ,

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