Question

X square minus y square is equal to X + y

Answer 1

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

Step-by-step explanation:

Let us solve the problem using multiplication of the two terms $(x+y)$ and $(x-y)$,

$\quad (x+y)(x-y)$

$=x(x-y)+y(x-y)$

• [ Using distributive property of multiplication over addition ]

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

• [ Since $(+)(+)=(+)$ and $(+)(-)=(-)$ ]

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

• [ Since multiplication of commutative, that is $yx=xy$ ]

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

• [ Since $a-a=0$ ]

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

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

Note:

The answer can be found by simply dividing $(x^{2}-y^{2})$ by $(x+y)$ using long division.