Resolver (3a+2b)(3a-2b)-(a-2b)^2

$$( 3 a + 2 b ) ( 3 a - 2 b ) - ( a - 2 b ) ^ { 2 }$$

Calcular

$$4\left(2a^{2}+ab-2b^{2}\right)$$

Pasos da solución

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

$$\left(3a\right)^{2}-\left(2b\right)^{2}-\left(a-2b\right)^{2}$$

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

$$3^{2}a^{2}-\left(2b\right)^{2}-\left(a-2b\right)^{2}$$

Calcula 3 á potencia de 2 e obtén 9.

$$9a^{2}-\left(2b\right)^{2}-\left(a-2b\right)^{2}$$

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

$$9a^{2}-2^{2}b^{2}-\left(a-2b\right)^{2}$$

Calcula 2 á potencia de 2 e obtén 4.

$$9a^{2}-4b^{2}-\left(a-2b\right)^{2}$$

Usar teorema binomial \left(p-q\right)^{2}=p^{2}-2pq+q^{2} para expandir \left(a-2b\right)^{2}.

$$9a^{2}-4b^{2}-\left(a^{2}-4ab+4b^{2}\right)$$

Para calcular o oposto de a^{2}-4ab+4b^{2}, calcula o oposto de cada termo.

$$9a^{2}-4b^{2}-a^{2}+4ab-4b^{2}$$

Combina 9a^{2} e -a^{2} para obter 8a^{2}.

$$8a^{2}-4b^{2}+4ab-4b^{2}$$

Combina -4b^{2} e -4b^{2} para obter -8b^{2}.

$$8a^{2}-8b^{2}+4ab$$

Expandir

$$8a^{2}+4ab-8b^{2}$$

Pasos da solución

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

$$\left(3a\right)^{2}-\left(2b\right)^{2}-\left(a-2b\right)^{2}$$

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

$$3^{2}a^{2}-\left(2b\right)^{2}-\left(a-2b\right)^{2}$$

Calcula 3 á potencia de 2 e obtén 9.

$$9a^{2}-\left(2b\right)^{2}-\left(a-2b\right)^{2}$$

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

$$9a^{2}-2^{2}b^{2}-\left(a-2b\right)^{2}$$

Calcula 2 á potencia de 2 e obtén 4.

$$9a^{2}-4b^{2}-\left(a-2b\right)^{2}$$

Usar teorema binomial \left(p-q\right)^{2}=p^{2}-2pq+q^{2} para expandir \left(a-2b\right)^{2}.

$$9a^{2}-4b^{2}-\left(a^{2}-4ab+4b^{2}\right)$$

Para calcular o oposto de a^{2}-4ab+4b^{2}, calcula o oposto de cada termo.

$$9a^{2}-4b^{2}-a^{2}+4ab-4b^{2}$$

Combina 9a^{2} e -a^{2} para obter 8a^{2}.

$$8a^{2}-4b^{2}+4ab-4b^{2}$$

Combina -4b^{2} e -4b^{2} para obter -8b^{2}.

$$8a^{2}-8b^{2}+4ab$$