Resol (2x+y)(2x-y)+(x+y)^2-2(x^2-xy)

Calcula

Expandiu

Prova

Algebra

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Copiat al porta-retalls

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

Considereu \left(2x+y\right)\left(2x-y\right). La multiplicació es pot transformar en una diferència de quadrats fent servir la regla: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Expandiu \left(2x\right)^{2}.

4x^{2}-y^{2}+\left(x+y\right)^{2}-2\left(x^{2}-xy\right)

Calculeu 2 elevat a 2 per obtenir 4.

4x^{2}-y^{2}+x^{2}+2xy+y^{2}-2\left(x^{2}-xy\right)

Utilitzeu el teorema del binomi \left(a+b\right)^{2}=a^{2}+2ab+b^{2} per desenvolupar \left(x+y\right)^{2}.

5x^{2}-y^{2}+2xy+y^{2}-2\left(x^{2}-xy\right)

Combineu 4x^{2} i x^{2} per obtenir 5x^{2}.

5x^{2}+2xy-2\left(x^{2}-xy\right)

Combineu -y^{2} i y^{2} per obtenir 0.

5x^{2}+2xy-2x^{2}+2xy

Utilitzeu la propietat distributiva per multiplicar -2 per x^{2}-xy.

3x^{2}+2xy+2xy

Combineu 5x^{2} i -2x^{2} per obtenir 3x^{2}.

3x^{2}+4xy

Combineu 2xy i 2xy per obtenir 4xy.