Resolver (2x-3y)^2-(2y+3x)(3x-2y)

$$( 2 x - 3 y ) ^ { 2 } - ( 2 y + 3 x ) ( 3 x - 2 y )$$

Calcular

$$13y^{2}-12xy-5x^{2}$$

Pasos da solución

Usar teorema binomial \left(a-b\right)^{2}=a^{2}-2ab+b^{2} para expandir \left(2x-3y\right)^{2}.

$$4x^{2}-12xy+9y^{2}-\left(2y+3x\right)\left(3x-2y\right)$$

Considera \left(2y+3x\right)\left(3x-2y\right). A multiplicación pódese transformar na diferencia de cadrados mediante a regra: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$4x^{2}-12xy+9y^{2}-\left(\left(3x\right)^{2}-\left(2y\right)^{2}\right)$$

Expande \left(3x\right)^{2}.

$$4x^{2}-12xy+9y^{2}-\left(3^{2}x^{2}-\left(2y\right)^{2}\right)$$

Calcula 3 á potencia de 2 e obtén 9.

$$4x^{2}-12xy+9y^{2}-\left(9x^{2}-\left(2y\right)^{2}\right)$$

Expande \left(2y\right)^{2}.

$$4x^{2}-12xy+9y^{2}-\left(9x^{2}-2^{2}y^{2}\right)$$

Calcula 2 á potencia de 2 e obtén 4.

$$4x^{2}-12xy+9y^{2}-\left(9x^{2}-4y^{2}\right)$$

Para calcular o oposto de 9x^{2}-4y^{2}, calcula o oposto de cada termo.

$$4x^{2}-12xy+9y^{2}-9x^{2}+4y^{2}$$

Combina 4x^{2} e -9x^{2} para obter -5x^{2}.

$$-5x^{2}-12xy+9y^{2}+4y^{2}$$

Combina 9y^{2} e 4y^{2} para obter 13y^{2}.

$$-5x^{2}-12xy+13y^{2}$$

Expandir

$$13y^{2}-12xy-5x^{2}$$

Pasos da solución

Usar teorema binomial \left(a-b\right)^{2}=a^{2}-2ab+b^{2} para expandir \left(2x-3y\right)^{2}.

$$4x^{2}-12xy+9y^{2}-\left(2y+3x\right)\left(3x-2y\right)$$

Considera \left(2y+3x\right)\left(3x-2y\right). A multiplicación pódese transformar na diferencia de cadrados mediante a regra: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$4x^{2}-12xy+9y^{2}-\left(\left(3x\right)^{2}-\left(2y\right)^{2}\right)$$

Expande \left(3x\right)^{2}.

$$4x^{2}-12xy+9y^{2}-\left(3^{2}x^{2}-\left(2y\right)^{2}\right)$$

Calcula 3 á potencia de 2 e obtén 9.

$$4x^{2}-12xy+9y^{2}-\left(9x^{2}-\left(2y\right)^{2}\right)$$

Expande \left(2y\right)^{2}.

$$4x^{2}-12xy+9y^{2}-\left(9x^{2}-2^{2}y^{2}\right)$$

Calcula 2 á potencia de 2 e obtén 4.

$$4x^{2}-12xy+9y^{2}-\left(9x^{2}-4y^{2}\right)$$

Para calcular o oposto de 9x^{2}-4y^{2}, calcula o oposto de cada termo.

$$4x^{2}-12xy+9y^{2}-9x^{2}+4y^{2}$$

Combina 4x^{2} e -9x^{2} para obter -5x^{2}.

$$-5x^{2}-12xy+9y^{2}+4y^{2}$$

Combina 9y^{2} e 4y^{2} para obter 13y^{2}.

$$-5x^{2}-12xy+13y^{2}$$