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Działania z matematyki RACHUNEK ALGEBRAICZNY

1.Doprowadz do najprostszej postaci wyrażenie:
-4(0.5ab+2.5a do potegi 2 b-3/8 ab do potegi 2) + 1 i 2/3(-6ab+9ab do potęgi 2)

2. Zmień iloczyn na sumy i zredukuj wyrazy podobne
a) (a-1)(a+2)
b) (2x-4)(5-8x)
c) (4ab-c)(2c+3ab)
d) (x-1)(x-2)(x-3)
e) (3x+1)*3x(3x-1)
f) -(2a+3b)(2a-2b)(a do potegi 2 - b do potegi 2)
g) (3a-4b+c)(5a+2b-5c)
h) (x do potegi 2 -1)(1+ x do potegi 2)(x-2)

3. Usuń naiwasy i zredukuj wyrazy podobne:
a)(3x-2)(y+3)-(x-3y)
b) (x+4)(y-5)-(3x-1)(y-2)+5xy
c) -21(x-1)+(4a-2)(x+5)
d) -[-(-(-x+y)(y-x)-(2x+y)(2y-x)]+4xy

Odpowiedź :

1.Doprowadz do najprostszej postaci wyrażenie:
-4(0.5ab+2.5a do potegi 2 b-3/8 ab do potegi 2) + 1 i 2/3(-6ab+9ab do potęgi 2)=-4(0,5ab+2,5a²b-3/8ab²)+5/3(-6ab+9ab²)=
=-2ab-10a²b+3/2ab²-10ab+15ab²=
=-12ab-10a²b+16,5ab²-10ab

2.
a) (a-1)(a+2)=a²+2a-a-2=a²+a-2
b) (2x-4)(5-8x)=10x-16x²-20+32x=-16x²+42x-20
c) (4ab-c)(2c+3ab)=8abc+12a²b²-2c²-3abc=12a²b²-2c²+5abc
d) (x-1)(x-2)(x-3)=x²-2x-x+2(x-3)=(x²-3x+2)(x-3)=x³-3x²-3x²+9x+2x-6=
=x³-6x²+11x-6
e) (3x+1)*3x(3x-1)=(3x+1)(9x²-3x)=27x³-9x²+9x²-3x=27x³-3x
f) -(2a+3b)(2a-2b)(a do potegi 2 - b do potegi 2)=
=-(4a²-4ab+6ab-6b²)(a²-b²)=-(4a²+2ab-6b²)(a²-b²)=
= (-4a²-2ab+6b²)(a²-b²)=
=-4a⁴+4a²b²-2a³b+2ab³+6a²b²-6b⁴=
=-4a⁴-6b⁴-2a³b+10a²b²+2ab³
g) (3a-4b+c)(5a+2b-5c)=
=15a²+6ab-15ac-20ab-8b²+20bc+5ac+2bc-5c²=
=15a²-8b²-5c²-14ab-10ac+22bc
h) (x do potegi 2 -1)(1+ x do potegi 2)(x-2)=
=(x²-1)(1+x²)(x-2)=
=(x²+x⁴-1-x²)(x-2)=
=(x⁴-1)(x-2)=
=x do 5-2x⁴-x+2

3.
a)(3x-2)(y+3)-(x-3y)=
=3xy+9x-2y-6-x+3y=
=3xy+8x+y-6
b) (x+4)(y-5)-(3x-1)(y-2)+5xy=
=xy-5x+4y-20-(3xy-6x-y+2)+5xy=
=xy-5x+4y-20-3xy+6x+y-2+5xy=
=3xy+x+5y-22
c) -21(x-1)+(4a-2)(x+5)=
=-21x+21+4ax+20a-2x-10=
=-23x+4ax+20a+11
d) -[-(-(-x+y)(y-x)-(2x+y)(2y-x)]+4xy=
=-[-(-(-xy+x²+y²-xy)-(4xy-2x²+2y²-xy)]+4xy=
=-[-(xy-x²-y²+xy)-4xy+2x²-2y²+xy]+4xy=
=-[-2xy+x²+y²-4xy+2x²-2y²+xy]+4xy=
=-[-5xy+3x²-y²]+4xy=
=-5xy-3x²+y²+4xy=
=-xy-3x²+y²
Roksi101viz
1. -4(0,5ab+2,5a² b- ⅜ab₂) + 1⅔(-6ab+9ab²) = -2ab - 10a²b + 1½ab² - 10ab + 15ab²= -12ab - 10a²b + 16,5ab²

2. a) (a-1)(a+2) = a² + 2a - a - 2= a² + a - 2
b)(2x-4)(5-8x) = 10x - 16x² - 20 + 32x= 42x - 16x² - 20
c) (4ab-c)(2c+3ab)=8abc+12a²b²-2c²-3abc= 5abc+12a²b²-2c²
d) (x-1)(x-2)(x-3)=(x²-2x-x+2)(x-3)=x³-3x²-2x²+6x-x²+3x+2x-6=x³-6x²+11x-6
e) (3x+1)×3x(3x-1)=(3x+1)(9x²-3x)=27x³-9x²+9x²-3x=27x³-3x
f) -(2a+3b)(2a-2b)(a² - b²)=(-2a-3b)(2a-2b)(a² - b²)= (-4a²+4ab-6ab+6b²)(a² - b²)= -4a⁴+10a²b²-2a³b+2ab³+-6b⁴
g) (3a-4b+c)(5a+2b-5c)=15a²-10ac-14ab-8b²+24bc-5c²
h) (x² -1)(1+ x²)(x-2)=(x²+x⁴-1-x²)(x-2)=x⁵-2x⁴-x+2

3. a)(3x-2)(y+3)-(x-3y)=3xy-9x-2y-6-x+6y= 3xy-10x+4y-6
b) (x+4)(y-5)-(3x-1)(y-2)+5xy=xy-5x+4y-20-3xy-6x+y-2+5xy= 3xy-11x+5y-22
c) -21(x-1)+(4a-2)(x+5)=-21x+21+4ax+20a-2x-10= -23x+11+4ax+20a
d) -[-(-(-x+y)(y-x)-(2x+y)(2y-x)]+4xy=2xy-y²+x²
Annaa300viz
1.Doprowadz do najprostszej postaci wyrażenie:
-4(0.5ab+2.5a do potegi 2 b-3/8 ab do potegi 2) + 1 i 2/3(-6ab+9ab do potęgi 2)=-4(0,5ab+2,5a²b-3/8ab²)+5/3(-6ab+9ab²)=
=-2ab-10a²b+3/2ab²-10ab+15ab²=
=-12ab-10a²b+16,5ab²-10ab

2.
a) (a-1)(a+2)=a²+2a-a-2=a²+a-2

b) (2x-4)(5-8x)=10x-16x²-20+32x=-16x²+42x-20

c) (4ab-c)(2c+3ab)=8abc+12a²b²-2c²-3abc=12a²b²-2c²+5abc

d) (x-1)(x-2)(x-3)=
=(x²-2x-x+2)(x-3)=
=(x²-3x+2)(x-3)=
=x³-3x²-3x²+9x+2x-6=
=x³-6x²+11x-6
e) (3x+1)*3x(3x-1)=
=(3x+1)(9x²-3x)=
=27x³-9x²+9x²-3x=
=27x³-3x
f) -(2a+3b)(2a-2b)(a do potegi 2 - b do potegi 2)=
=-(4a²-4ab+6ab-6b²)(a²-b²)=
= (-4a²-2ab+6b²)(a²-b²)=
=-4a⁴+4a²b²-2a³b+2ab³+6a²b²-6b⁴=
=-4a⁴-6b⁴-2a³b+10a²b²+2ab³
g) (3a-4b+c)(5a+2b-5c)=
=15a²+6ab-15ac-20ab-8b²+20bc+5ac+2bc-5c²=
=15a²-8b²-5c²-14ab-10ac+22bc

h) (x do potegi 2 -1)(1+ x do potegi 2)(x-2)=
=(x²-1)(1+x²)(x-2)=
=(x⁴-1)(x-2)=
=x do 5-2x⁴-x+2

3.
a)(3x-2)(y+3)-(x-3y)=
=3xy+9x-2y-6-x+3y=
=3xy+8x+y-6

b) (x+4)(y-5)-(3x-1)(y-2)+5xy=
=xy-5x+4y-20-(3xy-6x-y+2)+5xy=
=xy-5x+4y-20-3xy+6x+y-2+5xy=
=3xy+x+5y-22

c) -21(x-1)+(4a-2)(x+5)=
=-21x+21+4ax+20a-2x-10=
=-23x+4ax+20a+11

d) -[-(-(-x+y)(y-x)-(2x+y)(2y-x)]+4xy=
=-[-(-(-xy+x²+y²-xy)-(4xy-2x²+2y²-xy)]+4xy=
=-[-(xy-x²-y²+xy)-4xy+2x²-2y²+xy]+4xy=
=-[-2xy+x²+y²-4xy+2x²-2y²+xy]+4xy=
=-[-5xy+3x²-y²]+4xy=
=-5xy-3x²+y²+4xy=
=-xy-3x²+y²

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