Вправи: 232

232. Спростіть вираз:

1) (b\a+ba- b + a\a-ba+ b) • (a2\a2b2 + b2\b2a2 – 2\a2b2) : a4-b4 a2b2 = ab+ b2+a2- ab (a- b)(a+ b) • a4+b4-2a2b2 a2b2 • a2b2a4-b4 = (a2+b2)• (a4-2a2b4)•a2b2 a- ba+ b• a2b2• (a4- b4) = (a2+b2)(a2-b2)2 a- ba+ b(a2-b2)(a2+b2) = a2-b2 a2- b2 = 1;

2) (m² – n² – 4m2n-4mn2 m+ n) : (mm+ n – nn- m – 2mnm2-n2) = (m2-n2\m+n 1 – 4m2n-4mn2 m+ n) : (m\m-nm+ n + n\m+nm- n – 2mnm- n(m+ n)) = (m2-n2)(m+ n)- 4m2n+4mn2 m+ n : m2- mn+ mn+n2-2mn (m- n)(m+ n) = m- nm+ nm+ n-4mn(m- n)m+ n : (m- n)2(m- n)(m+ n) = (m- n)((m+ n)2-4mn)m+ n : m- nm+ n = m- n(m2+2mn+n2-4mn) m+ n • m+ nm- n = m- n(m2-2mn+ n2)•(m+ n)(m+ n)(m- n) = (m – n)².