Resolver (2a-1)(a-7)(+6a-3)(2a-1)

$$( 2 a - 1 ) ( a - 7 ) ( + 6 a - 3 ) ( 2 a - 1 )$$

Calcular

$$3\left(a-7\right)\left(2a-1\right)^{3}$$

Pasos da solución

Multiplica 2a-1 e 2a-1 para obter \left(2a-1\right)^{2}.

$$\left(2a-1\right)^{2}\left(a-7\right)\left(6a-3\right)$$

Usar teorema binomial \left(p-q\right)^{2}=p^{2}-2pq+q^{2} para expandir \left(2a-1\right)^{2}.

$$\left(4a^{2}-4a+1\right)\left(a-7\right)\left(6a-3\right)$$

Aplicar a propiedade distributiva multiplicando cada termo de 4a^{2}-4a+1 por cada termo de a-7.

$$\left(4a^{3}-28a^{2}-4a^{2}+28a+a-7\right)\left(6a-3\right)$$

Combina -28a^{2} e -4a^{2} para obter -32a^{2}.

$$\left(4a^{3}-32a^{2}+28a+a-7\right)\left(6a-3\right)$$

Combina 28a e a para obter 29a.

$$\left(4a^{3}-32a^{2}+29a-7\right)\left(6a-3\right)$$

Aplicar a propiedade distributiva multiplicando cada termo de 4a^{3}-32a^{2}+29a-7 por cada termo de 6a-3.

$$24a^{4}-12a^{3}-192a^{3}+96a^{2}+174a^{2}-87a-42a+21$$

Combina -12a^{3} e -192a^{3} para obter -204a^{3}.

$$24a^{4}-204a^{3}+96a^{2}+174a^{2}-87a-42a+21$$

Combina 96a^{2} e 174a^{2} para obter 270a^{2}.

$$24a^{4}-204a^{3}+270a^{2}-87a-42a+21$$

Combina -87a e -42a para obter -129a.

$$24a^{4}-204a^{3}+270a^{2}-129a+21$$

Expandir

$$24a^{4}-204a^{3}+270a^{2}-129a+21$$

Pasos da solución

Multiplica 2a-1 e 2a-1 para obter \left(2a-1\right)^{2}.

$$\left(2a-1\right)^{2}\left(a-7\right)\left(6a-3\right)$$

Usar teorema binomial \left(p-q\right)^{2}=p^{2}-2pq+q^{2} para expandir \left(2a-1\right)^{2}.

$$\left(4a^{2}-4a+1\right)\left(a-7\right)\left(6a-3\right)$$

Aplicar a propiedade distributiva multiplicando cada termo de 4a^{2}-4a+1 por cada termo de a-7.

$$\left(4a^{3}-28a^{2}-4a^{2}+28a+a-7\right)\left(6a-3\right)$$

Combina -28a^{2} e -4a^{2} para obter -32a^{2}.

$$\left(4a^{3}-32a^{2}+28a+a-7\right)\left(6a-3\right)$$

Combina 28a e a para obter 29a.

$$\left(4a^{3}-32a^{2}+29a-7\right)\left(6a-3\right)$$

Aplicar a propiedade distributiva multiplicando cada termo de 4a^{3}-32a^{2}+29a-7 por cada termo de 6a-3.

$$24a^{4}-12a^{3}-192a^{3}+96a^{2}+174a^{2}-87a-42a+21$$

Combina -12a^{3} e -192a^{3} para obter -204a^{3}.

$$24a^{4}-204a^{3}+96a^{2}+174a^{2}-87a-42a+21$$

Combina 96a^{2} e 174a^{2} para obter 270a^{2}.

$$24a^{4}-204a^{3}+270a^{2}-87a-42a+21$$

Combina -87a e -42a para obter -129a.

$$24a^{4}-204a^{3}+270a^{2}-129a+21$$