Question

Zad.1
Zapisz w postaci iloczynu lub potęgi.
a) z² - 8z + 16
b) 1/4 + t +t²
c) y² - 1/25
d) 9b² - 16a²

zad.2
Zredukuj wyrazy podobne.
a) 5x - 3y + 8x + 7y
b) (10a - 3b + 5) - (4a + 7b - 15)
c) (5z² - 4z) - (2z - 3z² + 6)
d) -(3ab - 7b + 11) + (9 + 4b + 6ab)
e) (x-2) (x+1)
f) (3y - 4) (5 - 2y)
g) (z - 7) (z + 7)
h) (a-1) (a-2) (a-3)

zad.3
Przedstaw w postaci sumy i zredukuj wyrazy podobne.
a) (b-2) (b+3) - (b+2) (b-3)
b) (z+4) (y-5) - (2z - 1) (y+2) - 7xy
c) (8t - 3) (y+4) - 7t( y+2)
d) (5a - 3b + 2c) (4a + 2b - c)
e) 2(a² - 3) + (2 - a) (a + 4)
f) -(2a² - 3) - (2a + 3) (2a - 3)
g) (x-4)² - (x-4) ( x+4)
h) (3 + 2x)² + 5(1- 3x)² - (2 + x) (2x - 3)

Bardzo prosze o pomoc ;p z gory dzieki ^^

Answer 1

Zad.1
a) z² - 8z + 16=(z-4)²
b) 1/4 + t +t²=(1/2+t)²
c) y² - 1/25=(y-1/5)(y+1/5)
d) 9b² - 16a²=(3b-4a)(3b+4a)

zad.2
Zredukuj wyrazy podobne.
a) 5x - 3y + 8x + 7y=13x+4y
b) (10a - 3b + 5) - (4a + 7b - 15)=10a - 3b + 5-4a - 7b +15=6a-10b+20
c) (5z² - 4z) - (2z - 3z² + 6)=5z² - 4z-2z+ 3z²- 6=8z²-6z-6
d) -(3ab - 7b + 11) + (9 + 4b + 6ab)=-3ab+ 7b- 11+9 + 4b + 6ab=3ab+11b-2
e) (x-2) (x+1)=x²+x-2x-2=x²-x-2
f) (3y - 4) (5 - 2y)=15y-6y²-20+8y=-6y²+23y-20
g) (z - 7) (z + 7)=z²-49
h) (a-1) (a-2) (a-3)=(a²-2a-a+2)(a-3)=a³-3a²+2a-3a²+6a-6=a³-6a²+8a

Answer 2

Zad.1
Zapisz w postaci iloczynu lub potęgi.
stosuje wzory skróconego mnożenia
a² -b² = ( a -b )( a +b)
(a - b)² =a²+2ab + b²
(a + b)² =a² -2ab +b²


a) z² - 8z + 16 = (z -4)²
b) 1/4 + t +t² = (1/2 + t)²
c) y² - 1/25 = (y - 1/5)(y + 1/5)
d) 9b² - 16a²= (3b - 4a)(3b +4)

zad.2
Zredukuj wyrazy podobne.
a) 5x - 3y + 8x + 7y =
= 13x +4y

b) (10a - 3b + 5) - (4a + 7b - 15)=
= 10a -3b +5 -4a -7b+15 =
=6a -10b+20

c) (5z² - 4z) - (2z - 3z² + 6)=
= 5z² - 4z -2z +3z² -6 =
=8z²- 6z -6

d) -(3ab - 7b + 11) + (9 + 4b + 6ab)=
= -3ab +7b -11 + 9+4b+ 6ab=
= 3ab +11b -2

e) (x-2) (x+1)=
=x² + x - 2x -2 =
= x² -x -2

f) (3y - 4) (5 - 2y)=
= 15y - 6y² -20+8y =
= 23y - 6y² - 20

g) (z - 7) (z + 7)=
= z² - 49

h) (a-1) (a-2) (a-3)=
= (a² -2a -a +2)(a -3)=
= (a²- 3a +2)(a-3) =
= a³ -3a² -3a² + 9a +2a -6 =
= a³ - 6a² + 11a - 6

zad.3
Przedstaw w postaci sumy i zredukuj wyrazy podobne.
a) (b-2) (b+3) - (b+2) (b-3)=
= (b² +3b - 2b -6 -( b² -3b + 2b -6) =
= b² +b -6 - b² +b+6=
= 2b

b) (z+4) (y-5) - (2z - 1) (y+2) - 7xy=
= (yz - 5z + 4y -20) -(2yz + 4z -y -2)=
= yz - 5z + 4y -20 - 2yz - 4z +y +2 =
= -3yz - 9z +5y -18

c) (8t - 3) (y+4) - 7t( y+2)=
= 8ty + 32t -3y-12 -7ty - 14t=
= ty + 18t -3y-12

d) (5a - 3b + 2c) (4a + 2b - c)=
= 20a² +10ab - 5ac -12ab -6b² - 3bc + 8ac+4bc - 2c²=
= 20a²-2ab+3ac - 6b² +bc- 2c²

e) 2(a² - 3) + (2 - a) (a + 4)=
= 2a² - 6 + 2a +8 -a² -4a=
= a² -2a +2

f) -(2a² - 3) - (2a + 3) (2a - 3)=
= -2a² +3 -(4a² -9)=
= -2a² +3 -4a² +9 =
= -6a² +12

g) (x-4)² - (x-4) ( x+4)=
= x² - 8x +16 -(x² -16)=
= x² -8x +16 -x² +16 =
= -8x +32

h) (3 + 2x)² + 5(1- 3x)² - (2 + x) (2x - 3)=
= 9 + 12x + 4x² + 5(1 -6x+ 9x²) - (4x - 6 +2x² -3x)=
= 9 + 12x + 4x² + 5 - 30x + 45x² - ( x -6 +2x²) =
= 9 + 12x + 4x² + 5 - 30x + 45x² -x +6 -2x² =
= 47x² -19x +11

Answer 3

1.
a) (z-4)²
b)(0,5+t)
c) (y-0,2)²

2.
a) 5x - 3y + 8x + 7y=
13x+4y
b) (10a - 3b + 5) - (4a + 7b - 15)=
10a-3b+5-4a-7b+15=
6a+10b+20
c) (5z² - 4z) - (2z - 3z² + 6)=
5z²-4z-2z+3z²-6=
8z²-6z-6
d) -(3ab - 7b + 11) + (9 + 4b + 6ab)=
-3ab+7b-11+9+4b+6ab=
3ab+11b-3
e) (x-2)*(x+1)=
x²+x-2x-2=
x²-x-2
f) (3y - 4) * (5 - 2y)=
15y-6y²-20+8y=
23y-6y²+20
g) (z - 7) * (z + 7)=
z²+7z-7z-49=
z²-49
h) (a-1) (a-2) (a-3)=
(a²-2a-a+2)*(a-3)=
a^3-2a²-a²+2a-3a²+6a+3a-6=
a^3-7a²+11a-6

3.
a) (b-2) (b+3) - (b+2) (b-3)=
b²+3b-2b-6-b²+3b-2b+6=
2b
b) (z+4) (y-5) - (2z - 1) (y+2) - 7xy
zy-5z+4y-20-(2zy+4z-y-2)-7xy=
zy-5z+4y-20-2zy-4z+y+2-7xy=
-zy-9z+5y-18-7xy
c) (8t - 3) (y+4) - 7t( y+2)=
8ty+32t-3y-12-7ty-14t=
ty+18-10y
d) (5a - 3b + 2c) (4a + 2b - c)=
20a²+8ab-5ac-12ab-6b²+3bc+8ac+4bc-2c²=
14a²-4ab+3ac+7bc-2c²
e) 2(a² - 3) + (2 - a) (a + 4)=
2a²-6+2a+8-a²-4a=
a²+2-2a
f) -(2a² - 3) - (2a + 3) (2a - 3)=
-2a² -3-(4a² -6a+6a-9)=
-2a² -3-4a² +6a-6a+9=
-6a² +6
g) (x-4)² - (x-4) ( x+4)=
x²-8x+16-(x²+4x-4x-16)=
x²-8x+16-x²-4x+4x+16=
-8x+32
h) (3 + 2x)² + 5(1- 3x)² - (2 + x) (2x - 3)=
9+12x+4x²+5(1-6x+9x²)-(4x-6+2x²-3x)=
9+12x+4x²+5-30x+45x²-4x+6-2x²+3x=
51x²-19x+20