Question

Упростить. | 37 баллов
$(a^{2}- b^{-1})^{2}+2a^{2}b^{-1}$

Answer 1

$(a^{2}- b^{-1})^{2}+2a^{2}b^{-1}=a^4-2a^{2}b^{-1}+b^{-2}+2a^{2}b^{-1}=a^4+b^{-2}$

Answer 2

${( {a}^{2} - {b}^{ - 1}) }^{2} + 2 {a}^{2} {b}^{ - 1} = {( {a}^{2} - \frac{1}{b} )}^{2} + 2 {a}^{2} \times \frac{1}{b} = {( \frac{ {a}^{2}b - 1 }{b})}^{2} + \frac{2 {a}^{2} \times 1}{b} = \frac{ {a}^{4} {b}^{2} - 2 {a}^{2}b + 1 }{ {b}^{2} } + \frac{2 {a}^{2} }{b} = \frac{ {a}^{4} {b}^{2} - 2 {a}^{2}b + 1 + 2 {a}^{2}b }{ {b}^{2} } = \frac{ {a}^{4} {b}^{2} + 1}{ {b}^{2} }$