How do you simplify $(x + y) (x - y)$ $(x + y)(x - y)$ ?

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Answer 1 · 2016-07-22T05:04:14

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

To simplify $(x + y) (x - y)$ $(x+y)(x-y)$ we use distributive property of number systems.

Let us treat $(x + y)$ $(x+y)$ as a single number and distribute it over $(x - y)$ $(x-y)$ .

This makes $(x + y) (x - y)$ $(x+y)(x-y)$

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

Now using commutative property of multiplication the above is equivalent to

$x (x + y) - y (x + y)$ $x(x+y)-y(x+y)$ and now again using distributive property this is equivalent to

$x \times x + x \times y - y \times x - y \times y$ $x xx x+x xx y- y xx x-yxxy$

$x \times x + x \times y - x \times y - y \times y$ $x xx x+x xx y- x xx y-yxxy$

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

= $x^2+cancel(xy)-cancel(xy)-y^2$

= $x^2-y^2$

How do you simplify (x + y)(x - y)(x+y)(x−y)(x + y)(x - y)?