Question

For any real number x and y,the square of their sum is equal to the sum of their squares plus twice their product?true or false?

Answer 1

Answer

yes

Step-by-step explanation:

(x+y)^2=(x+y)(x+y)

                 =x(x+y)+y(x+y)

                 =x^2+xy+xy+y^2

                  =x^2+2xy+y^2

So ,the square of their sum is equal to the sum of their squares plus twice their product

Answer 2

Answer:

This statement is true

Step-by-step explanation:

Given:

Two numbers are x and y

Sum of two number = x+y

Square of their sum = $(x + y)^{2}$

Product of the numbers= xy

According to the problem we have to prove that ,

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

As we know that,$(x +y)^{2} =x^{2} +y^{2} +2xy$

So,L.H.S

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

L.H.S =R.H.S