1. Zapisz w jak najprostszej postaci podane wyrażenia . a ) x+[x - ( z - x ) ] b ) - ( - a ) + ( -b + a ) c ) a - [ b - ( a + b ) ] d ) x - { x - [ x - ( x + 1 ) - ( x - 1 ) - x ] + ( 1 - x ) } 2. Przekształć iloczyny . a ) 3(a - 2 ) b) -4(x + y ) c) -5( -x + 1 ) d) - 3a (1/3 - a ) e) ( t-2s-1) *7 f) 1/2 ( 2a + 4b + 1 ) g) m ( 2m + 3 ) h) 3p(2r + 5p - 1 ) i ) xy ( 2x - 3y + 5 )
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a).x+[x-(z-x)] = x+(x-z+x) = x+(2x-z) = x+2x-z = 3x-z
b).-(-a)+(-b+a) = a-b+a = 2a-b
c).a-[b-(a+b)] = a-(b-a-b) = a+a = 2a
d).x-{x-[x-(x+1)-(x-1)-x]+(1-x)} = x-{x-(x-x-1-x+1-x)+1-x} = x-{x-(-2x)+1-x} =
= x-[(x+2x)+1-x] = x-(3x+1-x) = x-(2x+1) = x-2x-1 = -x-1
Zad 2
a).3(a-2) = 3a-6
b).-4(x+y) = -4x-4y
c).-5(-x+1) = 5x-5
d).-3a(1/3 -a) = -a+3a²
e).(t-2s-1) * 7 = 7t-14s-7
f).1/2(2a+4b+1) = a+2b+1/2
g).m(2m+3) = 2m²+3m
h).3p(2r+5p-1) = 6pr+15p²-3p
i).xy(2x-3y+5) = 2x²y-3xy²+5xy