Question

Rút gọn biểu thức

( x + y)² - ( x - y )² + (x+y)(x+y)

Answer 1

Ta có: (x+y)² - (x-y)² + (x+y)(x+y)

= (x² + 2xy + y²) - (x² - 2xy + y²) + (x+y)(x+y)

= x² + 2xy + y² - x² +2xy - y² + x² +xy + xy + y²

= x² + y² + 2xy + 2xy + xy + xy

= x² + y² + 6xy.

= (x² + 2xy + y²) + 4xy

= (x+y)² + 4xy.

Answer 2

\(\left(x+y\right)^2-\left(x-y\right)^2+\left(x+y\right)\left(x+y\right)\)

\(=\left(x+y-x+y\right)+\left(x^2+xy+xy+y^2\right)\)

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