Question

Wyrażenia algebraiczne!!!

a)(a-2)do potęgi 2+(3a+1)do potęgi 2 dla a=3

b)(b+4)(b-4)-2(3-2b)do potęgi2 dlab=-2

c)3(c+1)do potęgi 2-(c+5)(5-c) dla c=1/2

d)2a(a-4)-3(a+3)do potęgi 2 dla a=-2

e)(b-1)(1+b)-2(b+3)(b-5) dla b=3

Answer 1

a) (a-2)² + (3a+1)² = a² - 4a +4 +9a² + 6a +1 = 10a² +2a +5 = 10*3² +2*3 +5 = 10*9 + 6 + 5 = 90+ 11 = 101

b) (b+4)(b-4)-2(3-2b)² = b² - 4² - 2(3² - 12b +4b²) = b² - 16 -2(9 - 12b +4b²) = b² - 16 -18 +24b - 8b² = -7b² +24b - 34 = -7*(-2)² +24*(-2) - 34 = -7*4 -48 -34 = -28 - 48 - 34 = - 110

c) 3(c+1)²-(c+5)(5-c) = 3(c² +2c +1)-(5+c)(5-c) = 3c² + 6c + 3 - (5² - c²) = 3c² +6c + 3 - 25 + c² = 4c² +6c - 22 = 4*(½)² + 6*½ - 22 = 4*¼ + 3 - 22 = 1+3-22 = 4 - 22 = -18

d) 2a(a-4)-3(a+3)² = 2a² - 8a - 3(a² + 6a +3²) = 2a² - 8a -3(a² + 6a +9) = 2a² - 8a - 3a² - 18a -27 = -a² - 26a - 27 = -(-2)² - 26*(-2) - 27 = -4 +52 - 27 = 52 - 31 = 21

e) (b-1)(1+b)-2(b+3)(b-5) = (b-1)(b+1)-2(b+3)(b-5) = b² - 1 - 2(b² - 5b +3b -15) = b² - 1 - 2(b² - 2b -15) = b² - 1 - 2b² +4b +30 = -b² + 4b +29 = -3² +4*3 +29 = -9 +12 +29 = 12 + 20 = 32