Resolver (m-5n)(m+5n)+(5n-1)^2

$$( m - 5 n ) ( m + 5 n ) + ( 5 n - 1 ) ^ { 2 }$$

Calcular

$$m^{2}-10n+1$$

Pasos da solución

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

$$m^{2}-\left(5n\right)^{2}+\left(5n-1\right)^{2}$$

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

$$m^{2}-5^{2}n^{2}+\left(5n-1\right)^{2}$$

Calcula 5 á potencia de 2 e obtén 25.

$$m^{2}-25n^{2}+\left(5n-1\right)^{2}$$

Usar teorema binomial \left(a-b\right)^{2}=a^{2}-2ab+b^{2} para expandir \left(5n-1\right)^{2}.

$$m^{2}-25n^{2}+25n^{2}-10n+1$$

Combina -25n^{2} e 25n^{2} para obter 0.

$$m^{2}-10n+1$$

Expandir

$$m^{2}-10n+1$$

Pasos da solución

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

$$m^{2}-\left(5n\right)^{2}+\left(5n-1\right)^{2}$$

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

$$m^{2}-5^{2}n^{2}+\left(5n-1\right)^{2}$$

Calcula 5 á potencia de 2 e obtén 25.

$$m^{2}-25n^{2}+\left(5n-1\right)^{2}$$

Usar teorema binomial \left(a-b\right)^{2}=a^{2}-2ab+b^{2} para expandir \left(5n-1\right)^{2}.

$$m^{2}-25n^{2}+25n^{2}-10n+1$$

Combina -25n^{2} e 25n^{2} para obter 0.

$$m^{2}-10n+1$$