Вправи: 409 (1-3)

409. Спростіть вираз:

1) (b-3-1b+1)^–2 • (2b+2b-2+b-1+1)^–2 = (b+1b-3-1)² • (b-2+b-1+1 2b+2)² = (b+1)2(1b3-1)2 • (1b2+ 1b+1)2(2(b+1)2 = (1+ b+b2b2)24(1-b3b3)2 = (1+ b+ b2b2)2 4•((1- b)(1+ b+b2)b3)2 = (1+ b+ b2)2•(b3)2 (b2)2•4• (1- b)2(1+ b+ b2)2 = b24(1- b)2;

2) (a(ab)^–2)^–1 : ((ab)^–1b)² = (a(ba)²)^–1 : (ba • b)² = (b2a)^–1 : (b2a)² = ab2 • a2b4 = a3b6;

3) ((nm)^–2 – (mn)^–2) • (mn)² = ((mn)² – (nm)²) • (mn)² = (m2n2 – n2m2) • m²n² = m⁴ – n⁴;

4) x-1+y-1 x-1- y-1 – x-1-y-1 x-1+y-1 = 1x+1y 1x- 1y – 1x-1y 1x+1y = y+ xxyy- xxy – y- xxyy+ xxy = y+ x• xyxy(y- x) – y- x• xyxy•(y+ x) = y+ xy- x – y- xy+ x = (y+ x)2-(y- x)2 y- x(y+ x) = y2+2yx+x2-(y2-2yx+ x2) y2- x2 = y2+2yx+ x2-y2+2yx-x2 y2- x2 = 4xyy2- x2;

5) n1+ n2+n3+n4 n-1+ n-2+ n-3+n-4 = n1+n2+ n3+n4 1n+1n2+1n3+1n4 = n+n2+n3+ n4 n3+n2+ n+1 n4 = n•1+ n+ n2+ n3• n4n3+n2+ n+1 = n⁵;

6) xy-9+x-9y x-2y8+ x8y-2 = x-9y-9(x1-(-9)+y1-(-9)) x-2y-2(y8-(-2)+ x8-(-2)) = x-9y-9(x10+y10) x-2y-2(y10+ x10) = x^–7y^–7.