Question

Answer helpme please

Show that (x+y)² − (x −y)² = 4xy for all real numbers x and y.


I have sended 40 points. Plese help

Answer 1

To show:-

(x+y)² − (x −y)² = 4xy

Using difference of square identity:-

$a^2-b^2=(a-b)(a+b)$

Now ,taking left side

$\Rightarrow (x+y)^2-(x-y)^2$

⇒(x+ya , x+yb)

⇒(x+y-x+y)

⇒(x+y+x−y)

⇒(2x)(2y)

⇒4xy

Hence Proved!!!

$(x+y)^2-(x-y)^2=4xy$

Answer 2

Answer:

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

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

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

$= 4xy$

Now step by step explanation

we know the formula put the formulaof x+y whole square and x-y whole square.

Cancel out positive x and y square and negative x and y.

Then the result is 4 xy.

Hope it helps