Resolver (5x-7y)(5x+7y)+(7x-5y)(7x+5y)

$$( 5 x - 7 y ) ( 5 x + 7 y ) + ( 7 x - 5 y ) ( 7 x + 5 y )$$

Calcular

$$74\left(x^{2}-y^{2}\right)$$

Pasos da solución

Considera \left(5x-7y\right)\left(5x+7y\right). A multiplicación pódese transformar na diferencia de cadrados mediante a regra: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Expande \left(5x\right)^{2}.

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

Calcula 5 á potencia de 2 e obtén 25.

$$25x^{2}-\left(7y\right)^{2}+\left(7x-5y\right)\left(7x+5y\right)$$

Expande \left(7y\right)^{2}.

$$25x^{2}-7^{2}y^{2}+\left(7x-5y\right)\left(7x+5y\right)$$

Calcula 7 á potencia de 2 e obtén 49.

$$25x^{2}-49y^{2}+\left(7x-5y\right)\left(7x+5y\right)$$

Considera \left(7x-5y\right)\left(7x+5y\right). A multiplicación pódese transformar na diferencia de cadrados mediante a regra: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$25x^{2}-49y^{2}+\left(7x\right)^{2}-\left(5y\right)^{2}$$

Expande \left(7x\right)^{2}.

$$25x^{2}-49y^{2}+7^{2}x^{2}-\left(5y\right)^{2}$$

Calcula 7 á potencia de 2 e obtén 49.

$$25x^{2}-49y^{2}+49x^{2}-\left(5y\right)^{2}$$

Expande \left(5y\right)^{2}.

$$25x^{2}-49y^{2}+49x^{2}-5^{2}y^{2}$$

Calcula 5 á potencia de 2 e obtén 25.

$$25x^{2}-49y^{2}+49x^{2}-25y^{2}$$

Combina 25x^{2} e 49x^{2} para obter 74x^{2}.

$$74x^{2}-49y^{2}-25y^{2}$$

Combina -49y^{2} e -25y^{2} para obter -74y^{2}.

$$74x^{2}-74y^{2}$$

Expandir

$$74x^{2}-74y^{2}$$

Pasos da solución

Considera \left(5x-7y\right)\left(5x+7y\right). A multiplicación pódese transformar na diferencia de cadrados mediante a regra: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Expande \left(5x\right)^{2}.

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

Calcula 5 á potencia de 2 e obtén 25.

$$25x^{2}-\left(7y\right)^{2}+\left(7x-5y\right)\left(7x+5y\right)$$

Expande \left(7y\right)^{2}.

$$25x^{2}-7^{2}y^{2}+\left(7x-5y\right)\left(7x+5y\right)$$

Calcula 7 á potencia de 2 e obtén 49.

$$25x^{2}-49y^{2}+\left(7x-5y\right)\left(7x+5y\right)$$

Considera \left(7x-5y\right)\left(7x+5y\right). A multiplicación pódese transformar na diferencia de cadrados mediante a regra: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$25x^{2}-49y^{2}+\left(7x\right)^{2}-\left(5y\right)^{2}$$

Expande \left(7x\right)^{2}.

$$25x^{2}-49y^{2}+7^{2}x^{2}-\left(5y\right)^{2}$$

Calcula 7 á potencia de 2 e obtén 49.

$$25x^{2}-49y^{2}+49x^{2}-\left(5y\right)^{2}$$

Expande \left(5y\right)^{2}.

$$25x^{2}-49y^{2}+49x^{2}-5^{2}y^{2}$$

Calcula 5 á potencia de 2 e obtén 25.

$$25x^{2}-49y^{2}+49x^{2}-25y^{2}$$

Combina 25x^{2} e 49x^{2} para obter 74x^{2}.

$$74x^{2}-49y^{2}-25y^{2}$$

Combina -49y^{2} e -25y^{2} para obter -74y^{2}.

$$74x^{2}-74y^{2}$$