Odpowiedzi

2009-12-17T14:11:44+01:00
A) (x+3y)^-9y^ =x^+6xy+9y^-9y^=x^+6xy=x(x+6y)
b) (b+3)^-(b-3)^ =b^+6b+9-b^+6b-9^=12b
c) 2(3+b)^-12b =18+12b+2b^-12b=18+2b^=2(9+b^)
d) (3x-2)^+2(x+3)^ =9x^-12x+4+2x^+12x+18=22+11x^=11(2+x^)
1 1 1
2009-12-17T14:21:57+01:00
[x+3y)²-9y²=x²+6xy+9y²-9y²=x²+6xy
[b+3]²-[b-3]²=b²+6b+9-[b²-6b+9]=b²+6b+9-b²+6b-9=12b
2[3+b]²-12b=2[9+6b+b²]-12b=18+12b+2b-12b=18+2b
[3x-2]²+2[x+3]²=9x²-12x+4+2[x²+6x+9]=9x²-12x+4+2x²+12x+18=11x²+22
2009-12-17T14:26:31+01:00
A) (x+3y)^-9y^ =
b) (b+3)^-(b-3)^ =
c) 2(3+b)^-12b =
d) (3x-2)^+2(x+3)^ =

Należy wykorzystać wzory skróconego mnożenia:
(x + y)² =x² +2xy +y²
(x - y)² = x² - 2 xy +y²

a) (x+3y)^-9y^ = x² +2*x*3y +(3y)² - 9y² = x² +6xy +9y² - 9y² =
x² +6xy = x(x +6y)

b) (b+3)^-(b-3)^ = b² + 2*b*3 +3² - (b² - 2*b*3 +3²) =
= b²+ 6b +9 - b² + 6b - 9 = 12b

c) 2(3+b)^-12b = 2(3² + 2*3*b +b²) - 12b = 2(9 + 6b + b²) - 12b =
= 18 +12b +2b² - 12b = 2b² + 18 = 2(b² + 9)

d) (3x-2)^+2(x+3)^ = (3x)² - 2*3x*2 +2² +2(x²+2*x*3 +3²)=
= 9x² - 12x + 4 + 2x² + 12x +18 = 11x² + 22 = 11(x² + 2)