Odpowiedź :
Odpowiedź:
1.
a) 3 (2m - 4) + 5 (3 - 4m) = 6m - 12 + 15 - 20m = - 14m + 3
b) - 3 (p² - 2r) - p (2p + r) = - 3p² + 6r - 2p² - pr = - 5p² + 6r - pr
c) 2x (5x - 3x²) - 4x² (2 - 3x) = 10x² - 6x³ - 8x² + 12x³ = 2x² + 6x³
d) -5a (3a - ab + 2) + 3 (5a² - 3b) = - 15a² -5a²b - 10a + 15a² - 9b =
= - 5a²b - 10a - 9b
e) 7 (2x - 3) - 5 (2 - x) + x + 1 = 14x - 21 - 10 + 5x + x + 1 = 20x - 30
f) 6a (a + 1) - 9 ) (a² - a) + 8a² = 6a² + 6a - 9a² + 9a + 8a² = 5a² + 15a
g) 2x² (x + 1) + x² (1 - x) + x² = 2x³ + 2x² + x² -x³ + x² = x³ + 4x²
h) k² (1 - 3k) + 3 (k² - 1) - (k² - 3) + 1 = k² - 3k³ + 3k² - 3 - k² + 3 + 1 =
= - 3k³ + 3k² + 1
i) 3a² (- a + 3) - 2a (4a + 1) - x² = - 3a³ + 9a² - 8a² - 2a - a² = - 3a³ - 2a
j) 4a (4a - 1) - 2a (4a² - a - 2) - 2a² = 16a² - 4a - 8a³ + 2a² + 4a - 2a² =
= - 8a³ + 16a²
2.
a) (a - 4) (a + 5) = a² + 5a - 4a - 20 = a² + a - 20
b) (7b + 3) (2 - 4b) = 14b - 28b² + 6 - 12b = - 28b² + 2b + 6
c) (- 3c + 2d) (2c - 6) = - 6c² + 18c + 4cd - 12d
d) (9s - 2t) (7t - s) = 63st - 9s²- 14t² + 2st = 65 st - 9s² - 14t²
e) (- 10m + 3n) (5n - 4) = - 50 mn + 40m + 15n² - 12n
f) (3kl + 8k) (4 - 2l) = 12kl - 6 kl² + 32k - 16kl = - 6kl² - 4 kl + 32k
g) (4xy + 3x) (2y + 5x²y) = 8xy² + 20x³y² + 6xy + 15x³y
h) (- 2p²r - 3p) (5pr - 3p²r²) = - 10p³r² + 6p⁴r³ - 15p² + 9p³r² =
= 6p⁴r³ - p³r² - 15p²
i) (a + 3) (a - 1) + (a - 7) (a + 5) = a² - a + 3a - 3 + a² + 5a - 7a - 35 =
= 2a² - 38
j) (2b - 5) (3 - 2b) - (3b + 2) (b - 6) =
= 6b - 4b² - 15 + 10b - 3b² + 18b - 2b + 12 = - 7b² + 32b - 3
k) - 7c² (5c - 4) + (3c²+c) (6 - 2c) = -35c³ + 28c² + 18c² - 6c³ + 6c - 2c² =
= - 41c³ + 44c² + 6c
l) 3m (m - 4) (5m + 2) - m (2m + 3) (4 - 3m) =
= 15m³ + 6m² - 60m² - 24m - 8m² + 6m³- 12m + 9m²=
= 21m³ - 53m² - 36m
m) - 2x (3x - 5y) - (x + 2y) (3x - y) = - 6x² + 10xy - 3x² + xy - 6xy + 2y² =
= - 9x² + 2y² + 5xy
Szczegółowe wyjaśnienie:
Odpowiedź:
zad1
a) =6m-12+15-20m=3-14m
b)=-3[tex]p^{2}[/tex]+6r-2[tex]p^{2}[/tex]-pr=6r-5[tex]p^{2}[/tex]-pr
c)=10[tex]x^{2}[/tex]-6[tex]x^{3}[/tex]-8[tex]x^{2}[/tex]+12[tex]x^{3}[/tex]=6[tex]x^{3}[/tex]-2[tex]x^{2}[/tex]
d)=-15[tex]a^{2}[/tex]+5[tex]a^{2}[/tex]b-10a+15[tex]a^{2}[/tex]-9b=5[tex]a^{2}[/tex]b-10a-9b
e)=14x-21-10+5x+x+1=20x-30
f)=6[tex]a^{2}[/tex]+6a-9[tex]a^{2}[/tex]+9a+8[tex]a^{2}[/tex]=5[tex]a^{2}[/tex]+15a
g)=2[tex]x^{3}[/tex]+2[tex]x^{2}[/tex]+[tex]x^{2}[/tex]-[tex]x^{3}[/tex]+[tex]x^{2}[/tex]=[tex]x^{3}[/tex]+4[tex]x^{2}[/tex]
h)=[tex]k^{2}[/tex]-3[tex]k^{3}[/tex]+3[tex]k^{3}[/tex]-1-[tex]k^{2}[/tex]+3+1=3
i)=-3[tex]a^{3}[/tex]+9[tex]a^{2}[/tex]-8[tex]a^{2}[/tex]-2a-[tex]a^{2}[/tex]=-3[tex]a^{3}[/tex]-2a
j)=16[tex]a^{2}[/tex]-4a-8[tex]a^{3}[/tex]+2[tex]a^{2}[/tex]+4a-2[tex]a^{2}[/tex]=-8[tex]a^{3}[/tex]+8[tex]a^{2}[/tex]
zad2
a)=[tex]a^{2}[/tex]+5a-4a-20=[tex]a^{2}[/tex]+a-20
b)=14b-28[tex]b^{2}[/tex]+6-12b=-28[tex]b^{2}[/tex]+2b+6
c)=-6[tex]c^{2}[/tex]+18c+4dc-12d
d)=63st-9[tex]s^{2}[/tex]-14[tex]t^{2}[/tex]+2st=61st-9[tex]s^{2}[/tex]-14[tex]t^{2}[/tex]
e)=-50mn+40m+15[tex]n^{2}[/tex]-12n
f)=12kl-6k[tex]l^{2}[/tex]+32k-16kl=-4kl-6k[tex]l^{2}[/tex]+32k
g)=8x[tex]y^{2}[/tex]+20[tex]x^{3}[/tex][tex]y^{2}[/tex]+6xy+15[tex]x^{3}[/tex]y
h)=-10[tex]p^{3}[/tex][tex]r^{2}[/tex]+6[tex]p^{4}[/tex][tex]r^{3}[/tex]-15[tex]p^{2}[/tex]r+9[tex]p^{3}[/tex][tex]r^{2}[/tex]=6[tex]p^{4}[/tex][tex]r^{3}[/tex]-[tex]p^{3}[/tex][tex]r^{2}[/tex]-15[tex]p^{2}[/tex]
i)=[tex]a^{2}[/tex]-a+3a-3+[tex]a^{2}[/tex]+5a-7a-35=2[tex]a^{2}[/tex]-38
j)=6b-4[tex]b^{2}[/tex]-15+10b-3[tex]b^{2}[/tex]+18b-2b+12=-7[tex]b^{2}[/tex]+32b-3
k)=-35[tex]c^{3}[/tex]+28[tex]c^{2}[/tex]+18[tex]c^{2}[/tex]-6[tex]c^{3}[/tex]+6c-2[tex]c^{2}[/tex]=-41[tex]c^{3}[/tex]+44[tex]c^{2}[/tex]+6c
l)=3m(5[tex]m^{2}[/tex]+2m-20m-8)-m(8m-6[tex]m^{2}[/tex]+12-9m)=15[tex]m^{3}[/tex]-54[tex]m^{2}[/tex]-24m-8[tex]m^{2}[/tex]+6[tex]m^{3}[/tex]-12m
+9[tex]m^{2}[/tex]=21[tex]m^{3}[/tex]-53[tex]m^{2}[/tex]-36m
m)=-6[tex]x^{2}[/tex]+10xy-3[tex]x^{2}[/tex]+xy-6xy+2[tex]y^{2}[/tex]=2[tex]y^{2}[/tex]-9[tex]x^{2}[/tex]+5xy
Szczegółowe wyjaśnienie: