Resolver (4a-5b)(4a+5b)-(4a+2b)(4a-3b)+(-5b)^2

$$( 4 a - 5 b ) ( 4 a + 5 b ) - ( 4 a + 2 b ) ( 4 a - 3 b ) + ( - 5 b ) ^ { 2 }$$

Calcular

$$2b\left(2a+3b\right)$$

Pasos da solución

Considera \left(4a-5b\right)\left(4a+5b\right). A multiplicación pódese transformar na diferencia de cadrados mediante a regra: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\left(4a\right)^{2}-\left(5b\right)^{2}-\left(4a+2b\right)\left(4a-3b\right)+\left(-5b\right)^{2}$$

Expande \left(4a\right)^{2}.

$$4^{2}a^{2}-\left(5b\right)^{2}-\left(4a+2b\right)\left(4a-3b\right)+\left(-5b\right)^{2}$$

Calcula 4 á potencia de 2 e obtén 16.

$$16a^{2}-\left(5b\right)^{2}-\left(4a+2b\right)\left(4a-3b\right)+\left(-5b\right)^{2}$$

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

$$16a^{2}-5^{2}b^{2}-\left(4a+2b\right)\left(4a-3b\right)+\left(-5b\right)^{2}$$

Calcula 5 á potencia de 2 e obtén 25.

$$16a^{2}-25b^{2}-\left(4a+2b\right)\left(4a-3b\right)+\left(-5b\right)^{2}$$

Usa a propiedade distributiva para multiplicar 4a+2b por 4a-3b e combina os termos semellantes.

$$16a^{2}-25b^{2}-\left(16a^{2}-4ab-6b^{2}\right)+\left(-5b\right)^{2}$$

Para calcular o oposto de 16a^{2}-4ab-6b^{2}, calcula o oposto de cada termo.

$$16a^{2}-25b^{2}-16a^{2}+4ab+6b^{2}+\left(-5b\right)^{2}$$

Combina 16a^{2} e -16a^{2} para obter 0.

$$-25b^{2}+4ab+6b^{2}+\left(-5b\right)^{2}$$

Combina -25b^{2} e 6b^{2} para obter -19b^{2}.

$$-19b^{2}+4ab+\left(-5b\right)^{2}$$

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

$$-19b^{2}+4ab+\left(-5\right)^{2}b^{2}$$

Calcula -5 á potencia de 2 e obtén 25.

$$-19b^{2}+4ab+25b^{2}$$

Combina -19b^{2} e 25b^{2} para obter 6b^{2}.

$$6b^{2}+4ab$$

Expandir

$$4ab+6b^{2}$$

Pasos da solución

Considera \left(4a-5b\right)\left(4a+5b\right). A multiplicación pódese transformar na diferencia de cadrados mediante a regra: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\left(4a\right)^{2}-\left(5b\right)^{2}-\left(4a+2b\right)\left(4a-3b\right)+\left(-5b\right)^{2}$$

Expande \left(4a\right)^{2}.

$$4^{2}a^{2}-\left(5b\right)^{2}-\left(4a+2b\right)\left(4a-3b\right)+\left(-5b\right)^{2}$$

Calcula 4 á potencia de 2 e obtén 16.

$$16a^{2}-\left(5b\right)^{2}-\left(4a+2b\right)\left(4a-3b\right)+\left(-5b\right)^{2}$$

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

$$16a^{2}-5^{2}b^{2}-\left(4a+2b\right)\left(4a-3b\right)+\left(-5b\right)^{2}$$

Calcula 5 á potencia de 2 e obtén 25.

$$16a^{2}-25b^{2}-\left(4a+2b\right)\left(4a-3b\right)+\left(-5b\right)^{2}$$

Usa a propiedade distributiva para multiplicar 4a+2b por 4a-3b e combina os termos semellantes.

$$16a^{2}-25b^{2}-\left(16a^{2}-4ab-6b^{2}\right)+\left(-5b\right)^{2}$$

Para calcular o oposto de 16a^{2}-4ab-6b^{2}, calcula o oposto de cada termo.

$$16a^{2}-25b^{2}-16a^{2}+4ab+6b^{2}+\left(-5b\right)^{2}$$

Combina 16a^{2} e -16a^{2} para obter 0.

$$-25b^{2}+4ab+6b^{2}+\left(-5b\right)^{2}$$

Combina -25b^{2} e 6b^{2} para obter -19b^{2}.

$$-19b^{2}+4ab+\left(-5b\right)^{2}$$

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

$$-19b^{2}+4ab+\left(-5\right)^{2}b^{2}$$

Calcula -5 á potencia de 2 e obtén 25.

$$-19b^{2}+4ab+25b^{2}$$

Combina -19b^{2} e 25b^{2} para obter 6b^{2}.

$$6b^{2}+4ab$$