Question

Упростите выражение :-b2c(4b-c2) (4b+c2) +16b4c

Answer 1

$- {b}^{2} \times c \times (4b - {c}^{2} ) \times (4b + {c}^{2} ) + 16 {b}^{4} \times c = - {b}^{2} \times c \times {( {(4b)}^{2} - {( {c}^{2} )}^{2} )} + 16 {b}^{4} \times c = - {b}^{2} \times c \times (16 {b}^{2} - {c}^{4} ) + 16 {b}^{4} \times c = - 16 {b}^{4} c + {b}^{2} {c}^{5} + 16 {b}^{4} c = {b}^{2} {c}^{5}$

здесь использовалась формула:

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