Question

CMR :

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

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

Thanks

Answer 1

a) (x + y)² = (x + y)(x + y) = x² + xy + xy + y² = x² + 2xy + y² (đpcm)

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

Answer 2

a) Ta có: \(VT=\left(x+y\right)^2\)

\(=\left(x+y\right)\cdot\left(x+y\right)\)

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

\(=x^2+2xy+y^2=VP\)(đpcm)

b) Ta có: \(VP=x^2-2xy+y^2\)

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

\(=x\left(x-y\right)-y\left(x-y\right)\)

\(=\left(x-y\right)\cdot\left(x-y\right)\)

\(=\left(x-y\right)^2=VT\)(đpcm)