Question

Wyznacz iloczyn. Oblicz wartość otrzymanego wyrażenia dla x=½

a) (x-2)(x+2)

b) (4x+1)(4x-1)

c) (10x²-1)(10x²+1)

d) (5-4x²)(4x²+5)

e) (x²-2x)(x²+2x)

f) (x/2-4x³)(x/2+4x³)

Answer 1

X=1/2

a) (x-2)(x+2)
(1/2 -2)(1/2 +2) = 1/4 +1-1 -4 =-3 i 3/4
b) (4x+1)(4x-1)
(4*1/2 +1)(4*1/2-1) = (2+1)(2-1) = 4-2+2-1=3
c) ^2 - do potęgi 2
(10x^2-1)(10x^2+1)
(10 *(1/2)^2 -1)(10 *(1/2)^2+1) = (10*1/4 -1)(10*1/4 +1) = (5/2-1)(5/2+1) = 25/4+ 5/2 - 5/2 -1 = 25/4-1 = 6 i 1/4 - 1= 5 i 1/4
d) (5-4x^2)(4x^2+5)
(5-4(1/2)^2)(4(1/2)^2+5) = (5-4(1/4))(4(1/4)+5) = (5-1)(1+5) = 5+25-1-5=24
e) (x^2-2x)(x^2+2x)
((1/2)^2-2*1/2)((1/2)^2+2*1/2) = (1/4-1)(1/4+1) = 1/16 +1/4 - 1/4 -1 = 1/16 -1 = - 15/16
f) (x/2-4x^3)(x/2+4x^3)
( 1/2 /2 - 4 (1/2)^3 ) ( 1/2 /2 +4 (1/2)^3 )  = (1/4 - 4* 1/8)*( 1/4 + 4* 1/8) = (1/4 - 1/2)( 1/4+ 1/2) = 1/16 + 1/8 - 1/8 - 1/4 = 1/16 - 1/4 = 1/16 - 4/16 = -13/16