Question

Get the right pair of algebraic identities. A B (A) (x -y) 2 (1) (x+y)(x2+y2 -xy) (B) x2 -y 2 (2) (x+y)(x-y) (3) (x2+y2 -2xy)​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

The correct option of answer A is (3) and answer B is (2).

Step-by-step explanation:

Given, Algebraic Identities are : (A) $(x-y)^{2}$ and (B) $x^{2} -y^{2}$.

(A)

We know that $(x-y)^{2}$ = (x-y)(x-y) = x(x-y) -y(x-y)

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

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

Hence, we can say that $(x-y)^{2}$ = $x^{2} +y^{2}$ - 2xy.

Thus the correct option is (3).

(B)

Adding -xy and +xy in $x^{2} -y^{2}$, we have

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

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

           = x(x+y) -y(x+y)

           = (x+y)(x-y)

Hence, we can say that $x^{2} -y^{2}$ = (x+y)(x-y)

Thus the correct option is (2).

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