Resolver left(5x-7yright)^2-(2x-y)*(2x+y)-left(3x+4yright)^2

$${ \left(5x-7y \right) }^{ 2 } -(2x-y) \times (2x+y)- { \left(3x+4y \right) }^{ 2 }$$

Calcular

$$12x^{2}-94xy+34y^{2}$$

Pasos da solución

Usar teorema binomial \left(a-b\right)^{2}=a^{2}-2ab+b^{2} para expandir \left(5x-7y\right)^{2}.

$$25x^{2}-70xy+49y^{2}-\left(2x-y\right)\left(2x+y\right)-\left(3x+4y\right)^{2}$$

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

$$25x^{2}-70xy+49y^{2}-\left(\left(2x\right)^{2}-y^{2}\right)-\left(3x+4y\right)^{2}$$

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

$$25x^{2}-70xy+49y^{2}-\left(2^{2}x^{2}-y^{2}\right)-\left(3x+4y\right)^{2}$$

Calcula 2 á potencia de 2 e obtén 4.

$$25x^{2}-70xy+49y^{2}-\left(4x^{2}-y^{2}\right)-\left(3x+4y\right)^{2}$$

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

$$25x^{2}-70xy+49y^{2}-4x^{2}+y^{2}-\left(3x+4y\right)^{2}$$

Combina 25x^{2} e -4x^{2} para obter 21x^{2}.

$$21x^{2}-70xy+49y^{2}+y^{2}-\left(3x+4y\right)^{2}$$

Combina 49y^{2} e y^{2} para obter 50y^{2}.

$$21x^{2}-70xy+50y^{2}-\left(3x+4y\right)^{2}$$

Usar teorema binomial \left(a+b\right)^{2}=a^{2}+2ab+b^{2} para expandir \left(3x+4y\right)^{2}.

$$21x^{2}-70xy+50y^{2}-\left(9x^{2}+24xy+16y^{2}\right)$$

Para calcular o oposto de 9x^{2}+24xy+16y^{2}, calcula o oposto de cada termo.

$$21x^{2}-70xy+50y^{2}-9x^{2}-24xy-16y^{2}$$

Combina 21x^{2} e -9x^{2} para obter 12x^{2}.

$$12x^{2}-70xy+50y^{2}-24xy-16y^{2}$$

Combina -70xy e -24xy para obter -94xy.

$$12x^{2}-94xy+50y^{2}-16y^{2}$$

Combina 50y^{2} e -16y^{2} para obter 34y^{2}.

$$12x^{2}-94xy+34y^{2}$$

Expandir

$$12x^{2}-94xy+34y^{2}$$

Pasos da solución

Usar teorema binomial \left(a-b\right)^{2}=a^{2}-2ab+b^{2} para expandir \left(5x-7y\right)^{2}.

$$25x^{2}-70xy+49y^{2}-\left(2x-y\right)\left(2x+y\right)-\left(3x+4y\right)^{2}$$

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

$$25x^{2}-70xy+49y^{2}-\left(\left(2x\right)^{2}-y^{2}\right)-\left(3x+4y\right)^{2}$$

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

$$25x^{2}-70xy+49y^{2}-\left(2^{2}x^{2}-y^{2}\right)-\left(3x+4y\right)^{2}$$

Calcula 2 á potencia de 2 e obtén 4.

$$25x^{2}-70xy+49y^{2}-\left(4x^{2}-y^{2}\right)-\left(3x+4y\right)^{2}$$

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

$$25x^{2}-70xy+49y^{2}-4x^{2}+y^{2}-\left(3x+4y\right)^{2}$$

Combina 25x^{2} e -4x^{2} para obter 21x^{2}.

$$21x^{2}-70xy+49y^{2}+y^{2}-\left(3x+4y\right)^{2}$$

Combina 49y^{2} e y^{2} para obter 50y^{2}.

$$21x^{2}-70xy+50y^{2}-\left(3x+4y\right)^{2}$$

Usar teorema binomial \left(a+b\right)^{2}=a^{2}+2ab+b^{2} para expandir \left(3x+4y\right)^{2}.

$$21x^{2}-70xy+50y^{2}-\left(9x^{2}+24xy+16y^{2}\right)$$

Para calcular o oposto de 9x^{2}+24xy+16y^{2}, calcula o oposto de cada termo.

$$21x^{2}-70xy+50y^{2}-9x^{2}-24xy-16y^{2}$$

Combina 21x^{2} e -9x^{2} para obter 12x^{2}.

$$12x^{2}-70xy+50y^{2}-24xy-16y^{2}$$

Combina -70xy e -24xy para obter -94xy.

$$12x^{2}-94xy+50y^{2}-16y^{2}$$

Combina 50y^{2} e -16y^{2} para obter 34y^{2}.

$$12x^{2}-94xy+34y^{2}$$