6.3E: Mazoezi
- Page ID
- 177854
Mazoezi hufanya kamili
Kuzidisha Polynomial na Monomial
Katika mazoezi yafuatayo, ongeze.
4\((w+10)\)
- Jibu
-
4w+40
6 (b+8)
-3 (a+7)
- Jibu
-
-3a—21
-5 (p+9)
2 (x-7)
- Jibu
-
2x-14
7 (y-4)
—3 (k—4)
- Jibu
-
-3k+12
-8 (j-5)
q (q+5)
- Jibu
-
\(q^{2}+5 q\)
(k+7)
-b (b+9)
- Jibu
-
\(-b^{2}-9 b\)
-y (y+3)
-x (x-10)
- Jibu
-
\(-x^{2}+10 x\)
-p (p-15)
6r (4r+s)
- Jibu
-
\(24 r^{2}+6 r s\)
5c (9c+d)
12x (x-10)
- Jibu
-
\(12 x^{2}-120 x\)
9m (m-11)
-9a (3a+5)
- Jibu
-
\(-27 a^{2}-45 a\)
-4p (2p+7)
3\(\left(p^{2}+10 p+25\right)\)
- Jibu
-
\(3 p^{2}+30 p+75\)
6\(\left(y^{2}+8 y+16\right)\)
\(-8 x\left(x^{2}+2 x-15\right)\)
- Jibu
-
\(-8 x^{3}-16 x^{2}+120 x\)
\(-5 t\left(t^{2}+3 t-18\right)\)
5\(q^{3}\left(q^{3}-2 q+6\right)\)
- Jibu
-
\(5 q^{6}-10 q^{4}+30 q^{3}\)
4\(x^{3}\left(x^{4}-3 x+7\right)\)
\(-8 y\left(y^{2}+2 y-15\right)\)
- Jibu
-
\(-8 y^{3}-16 y^{2}+120 y\)
\(-5 m\left(m^{2}+3 m-18\right)\)
5\(q^{3}\left(q^{2}-2 q+6\right)\)
- Jibu
-
\(5 q^{5}-10 q^{4}+30 q^{3}\)
9\(r^{3}\left(r^{2}-3 r+5\right)\)
\(-4 z^{2}\left(3 z^{2}+12 z-1\right)\)
- Jibu
-
\(-12 z^{4}-48 z^{3}+4 z^{2}\)
\(-3 x^{2}\left(7 x^{2}+10 x-1\right)\)
\((2 m-9) m\)
- Jibu
-
\(2 m^{2}-9 m\)
\((8 j-1) j\)
\((w-6) \cdot 8\)
- Jibu
-
\(8 w-48\)
\((k-4) \cdot 5\)
4\((x+10)\)
- Jibu
-
4x+40
6 (y+8)
15 (r-24)
- Jibu
-
15r-360
12 (mst-30)
—3 (m+11)
- Jibu
-
-3m-33
-4 (p+15)
-8 (z-5)
- Jibu
-
-8z+40
—3 (x-9)
u (u+5)
- Jibu
-
\(u^{2}+5 u\)
\(q(q+7)\)
\(n\left(n^{2}-3 n\right)\)
- Jibu
-
\(n^{3}-3 n^{2}\)
\(s\left(s^{2}-6 s\right)\)
6\(x(4 x+y)\)
- Jibu
-
\(24 x^{2}+6 x y\)
5a (9a+b)
5p (11p-5q)
- Jibu
-
\(55 p^{2}-25 p q\)
12\(u(3 u-4 v)\)
3\(\left(v^{2}+10 v+25\right)\)
- Jibu
-
\(3 v^{2}+30 v+75\)
6\(\left(x^{2}+8 x+16\right)\)
2\(n\left(4 n^{2}-4 n+1\right)\)
- Jibu
-
\(8 n^{3}-8 n^{2}+2 n\)
3\(r\left(2 r^{2}-6 r+2\right)\)
\(-8 y\left(y^{2}+2 y-15\right)\)
- Jibu
-
\(-8 y^{3}-16 y^{2}+120 y\)
\(-5 m\left(m^{2}+3 m-18\right)\)
5\(q^{3}\left(q^{2}-2 q+6\right)\)
- Jibu
-
\(5 q^{5}-10 q^{4}+30 q^{3}\)
9\(r^{3}\left(r^{2}-3 r+5\right)\)
\(-4 z^{2}\left(3 z^{2}+12 z-1\right)\)
- Jibu
-
\(-12 z^{4}-48 z^{3}+4 z^{2}\)
\(-3 x^{2}\left(7 x^{2}+10 x-1\right)\)
\((2 y-9) y\)
- Jibu
-
\(18 y^{2}-9 y\)
\((8 b-1) b\)
Kuzidisha Binomial na Binomial
Katika mazoezi yafuatayo, kuzidisha binomials zifuatazo kwa kutumia: ⓐ Mali ya Usambazaji ⓑ njia ya FOIL ⓒ Njia ya Wima.
(w+5) (w+7)
- Jibu
-
\(w^{2}+12 w+35\)
(y+9) (y+3)
(p+11) (p-4)
- Jibu
-
\(p^{2}+7 p-44\)
(q+4) (q-8)
Katika mazoezi yafuatayo, kuzidisha binomials. Tumia njia yoyote.
(x+8) (x+3)
- Jibu
-
\(x^{2}+11 x+24\)
(y+7) (y+4)
(y-6) (y-2)
- Jibu
-
\(y^{2}-8 y+12\)
(x-7) (x-2)
(w-4) (w+7)
- Jibu
-
\(w^{2}+3 w-28\)
\((q-5)(q+8)\)
(p+12) (p-5)
- Jibu
-
\(p^{2}+7 p-60\)
(m+11) (m-4)
(6p+5) (p+1)
- Jibu
-
\(6 p^{2}+11 p+5\)
\((7 m+1)(m+3)\)
(2t-9) (10t+1)
- Jibu
-
\(20 t^{2}-88 t-9\)
(3r-8) (11r+1)
(5x-y) (3x-6)
- Jibu
-
\(15 x^{2}-3 x y-30 x+6 y\)
(10a-b) (3a—4)
(a+b) (2a+3b)
- Jibu
-
\(2 a^{2}+5 a b+3 b^{2}\)
(r+s) (3r+2s)
(4z-y) (z-6)
- Jibu
-
\(4 z^{2}-24 z-z y+6 y\)
(5x-y) (x-4)
\(\left(x^{2}+3\right)(x+2)\)
- Jibu
-
\(x^{3}+2 x^{2}+3 x+6\)
\(\left(y^{2}-4\right)(y+3)\)
\(\left(x^{2}+8\right)\left(x^{2}-5\right)\)
- Jibu
-
\(x^{4}+3 x^{2}-40\)
\(\left(y^{2}-7\right)\left(y^{2}-4\right)\)
(5ab-1) (2ab+3)
- Jibu
-
\(10 a^{2} b^{2}+13 a b-3\)
(2xy+3) (3xy+2)
(6pq-3) (4pq-5)
- Jibu
-
\(24 p^{2} q^{2}-42 p q+15\)
(3rs-7) (3rs-4)
Kuzidisha Trinomial na Binomial
Katika mazoezi yafuatayo, kuzidisha kutumia ⓐ Mali ya Usambazaji ⓑ Njia ya Wima.
\((x+5)\left(x^{2}+4 x+3\right)\)
- Jibu
-
\(x^{3}+9 x^{2}+23 x+15\)
\((u+4)\left(u^{2}+3 u+2\right)\)
\((y+8)\left(4 y^{2}+y-7\right)\)
- Jibu
-
\(4 y^{3}+33 y^{2}+y-56\)
\((a+10)\left(3 a^{2}+a-5\right)\)
Katika mazoezi yafuatayo, ongeze. Tumia njia yoyote.
\((w-7)\left(w^{2}-9 w+10\right)\)
- Jibu
-
\(w^{3}-16 w^{2}+73 w-70\)
\((p-4)\left(p^{2}-6 p+9\right)\)
\((3 q+1)\left(q^{2}-4 q-5\right)\)
- Jibu
-
\(3 q^{3}-11 q^{2}-19 q-5\)
\((6 r+1)\left(r^{2}-7 r-9\right)\)
Mazoezi ya mchanganyiko
(10y-6) + (4y-7)
- Jibu
-
14y-13
(15p-4) + (3p-5)
\(\left(x^{2}-4 x-34\right)-\left(x^{2}+7 x-6\right)\)
- Jibu
-
-11x-28
\(\left(j^{2}-8 j-27\right)-\left(j^{2}+2 j-12\right)\)
5\(q\left(3 q^{2}-6 q+11\right)\)
- Jibu
-
\(15 q^{3}-30 q^{2}+55 q\)
8\(t\left(2 t^{2}-5 t+6\right)\)
(s-7) (s+9)
- Jibu
-
\(s^{2}+2 s-63\)
(x-5) (x+13)
\(\left(y^{2}-2 y\right)(y+1)\)
- Jibu
-
\(y^{3}-y^{2}-2 y\)
\(\left(a^{2}-3 a\right)(4 a+5)\)
\((3 n-4)\left(n^{2}+n-7\right)\)
- Jibu
-
\(3 n^{3}-n^{2}-25 n+28\)
\((6 k-1)\left(k^{2}+2 k-4\right)\)
\((7 p+10)(7 p-10)\)
- Jibu
-
\(49 p^{2}-100\)
(3y+8) (3y-8)
\(\left(4 m^{2}-3 m-7\right) m^{2}\)
- Jibu
-
\(4 m^{4}-3 m^{3}-7 m^{2}\)
\(\left(15 c^{2}-4 c+5\right) c^{4}\)
\((5 a+7 b)(5 a+7 b)\)
- Jibu
-
\(25 a^{2}+70 a b+49 b^{2}\)
(3x-11y) (3x-11y)
(4y+12z) (4y-12z)
- Jibu
-
\(16 y^{2}-144 z^{2}\)
kila siku Math
Hesabu ya akili Unaweza kutumia kuzidisha binomial kuzidisha idadi bila calculator. Sema unahitaji kuzidisha mara 13 15. Fikiria 13 kama 10+3 na 15 kama 10+5.
- Panua (10+3) (10+5) kwa njia ya FOIL.
- Panua 13·15 bila kutumia calculator.
- Njia ipi ni rahisi kwako? Kwa nini?
Hesabu ya akili Unaweza kutumia kuzidisha binomial kuzidisha idadi bila calculator. Sema unahitaji kuzidisha mara 18 17. Fikiria 18 kama 20—2 na 17 kama 20-3.
- Panua (20—2) (20-3) kwa njia ya FOIL.
- Kuzidisha 18·17 bila kutumia calculator.
- Njia ipi ni rahisi kwako? Kwa nini?
- Jibu
-
- 306
- 306
- Majibu yatatofautiana.
Mazoezi ya kuandika
Ni njia gani unapendelea kutumia wakati wa kuzidisha binomials mbili: Mali ya Usambazaji, njia ya FOIL, au Njia ya Wima? Kwa nini?
Ni njia gani unapendelea kutumia wakati wa kuzidisha trinomial kwa binomial: Mali ya Usambazaji au Njia ya Wima? Kwa nini?
- Jibu
-
Majibu yatatofautiana.
Panua zifuatazo:
\(\begin{array}{l}{(x+2)(x-2)} \\ {(y+7)(y-7)} \\ {(w+5)(w-5)}\end{array}\)
Eleza mfano unaoona katika majibu yako.
Panua zifuatazo:
\(\begin{array}{l}{(m-3)(m+3)} \\ {(n-10)(n+10)} \\ {(p-8)(p+8)}\end{array}\)
Eleza mfano unaoona katika majibu yako.
- Jibu
-
Majibu yanaweza kutofautiana.
Panua zifuatazo:
\(\begin{array}{l}{(p+3)(p+3)} \\ {(q+6)(q+6)} \\ {(r+1)(r+1)}\end{array}\)
Eleza mfano unaoona katika majibu yako.
Panua zifuatazo:
\(\begin{array}{l}{(x-4)(x-4)} \\ {(y-1)(y-1)} \\ {(z-7)(z-7)}\end{array}\)
Eleza mfano unaoona katika majibu yako.
- Jibu
-
Majibu yanaweza kutofautiana.
Self Check
Baada ya kukamilisha mazoezi, tumia orodha hii ili kutathmini ujuzi wako wa malengo ya sehemu hii.
b Orodha hii inakuambia nini kuhusu ujuzi wako wa sehemu hii? Ni hatua gani utachukua ili kuboresha?