Question

Which of the following expression is equivalent to (x+y)^2 ? There more than one correct answer.

A.x^2+y^2
B.(y+x)^2
C.x(x+y)+y(x+y)
D.(x-y)^2
E.(x+y)(x+y)

Answer 1

Answer:

B, C, E

Step-by-step explanation:

$Option A,\\x^2 + y^2$

If we were to consider expanding the expression ( x + y )^2, take a look at the procedure below;

$( x + y )^2 =\\( x + y )( x + y ) =\\x^2 + xy + yx + y^2 =\\\\x^2 + 2xy + y^2 \neq x^2 + y^2$

Thus, the first option is incorrect

$Option B,\\( y + x )^2 =\\( y + x )( y + x ) =\\y^2 + yx + xy + x^2 =\\\\x^2 + 2xy + y^2$

x^2 + 2xy + y^2 is similar to the result of the expansion of ( x + y )^2, so the second option is correct

$Option C,\\x( x + y ) + y ( x + y ) =\\( x + y )( x + y ) =\\\\( x + y )^2$

Grouping like terms, x( x + y ) + y( x + y ) = ( x + y )^2, and thus the third option is correct

$Option D,\\( x - y )^2 =\\( x - y )( x - y ) =\\x^2 - xy - yx + y^2 =\\\\x^2 - 2xy + y^2 \neq x^2 + 2xy + y^2$

As noted before, x^2 - 2xy + y^2 is not x^2 + 2xy + y^2, so the fourth option is incorrect

$Option E,\\( x + y )^2 = ( x + y )( x + y )$

And thus, Option E is correct!