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

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Algebra

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Copiado para a área de transferência

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

Considere \left(2x+y\right)\left(2x-y\right). A multiplicação pode ser transformada na diferença dos quadrados através da regra: \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)

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

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

Calcule 2 elevado a 2 e obtenha 4.

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

Utilize o teorema binomial \left(a+b\right)^{2}=a^{2}+2ab+b^{2} para expandir \left(x+y\right)^{2}.

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

Combine 4x^{2} e x^{2} para obter 5x^{2}.

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

Combine -y^{2} e y^{2} para obter 0.

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

Utilize a propriedade distributiva para multiplicar -2 por x^{2}-xy.

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

Combine 5x^{2} e -2x^{2} para obter 3x^{2}.

3x^{2}+4xy

Combine 2xy e 2xy para obter 4xy.