1. m=2√3-3√2 n=2√2+3√3.
a) m*n
b) (m-n)(m+n)
c) m²+m*n
d) m/n
2.przekształć wyrażenie korzystając ze wzorów skróconego mnozenia:
a.(0,5x²-3y)³
b. (ab²+2a)³
c. (1/2-3b)(1/4a²+3/2ab+9b²)
3. zapisz w postaci iloczynu:
a. (a+b)³-64
b.(1/3a+2)³+27
c. (2a-3)³-1/27

1

Odpowiedzi

2009-10-25T12:48:07+01:00
1.
a) (2√3-3√2)*(2√2+3√3)=4√6+18-12-9√6=6-5√6
b) [(2√3-3√2)-(2√2+3√3)] [(2√3-3√2)+(2√2+3√3)]=
[2√3-3√2-2√2-3√3)] [2√3-3√2+2√2+3√3]=(-√3-5√2)(5√3-√2)=
-15+√6-25√6+10=-5-24√6
c) (2√3-3√2)²+(2√3-3√2)(2√2+3√3)=12-12√6+18+4√6+18-12-9√6=36-17√6
d) 2√3-3√2 2√2-3√3 4√6-18-12+9√6 13√6-30 -13+30
--------- * -------- = --------------- = ---------- = -------
2√2+3√3 2√2-3√3 8-27 -19 19

2.
a.(0,5x²-3y)³= 0,125x⁶-3*0,25x⁴*3y+3*0,5x²*9y²-27y³=
0,125x⁶-2,25x⁴y+13,5x²y²-27y³
b. (ab²+2a)³=a³b⁶+3*a²b⁴*2a+3*ab²*4a²+8a³=
a³b⁶+6a³b⁴+12a³b²+8a³
c. (1/2-3b)(1/4a²+3/2ab+9b²)=(1/2)³-(3b)³=1/8-27b³

3.
a. (a+b)³-64=(a+b)³-4³= [(a+b)-4] [(a+b)²+4(a+b)+16] =
b.(1/3a+2)³+27 = [(1/3a+3)+3] [(1/3a)²-3(1/3a)+3] =
c. (2a-3)³-1/27 = [(2a-3)-1/3] [(2a-3)²+1/3(2a-3)+1/9]