6.3E: Mazoezi

Mazoezi hufanya kamili

Kuzidisha Polynomial na Monomial

Katika mazoezi yafuatayo, ongeze.

Zoezi$\PageIndex{1}$

4$(w+10)$

Jibu

4w+40

Zoezi$\PageIndex{2}$

6 (b+8)

Zoezi$\PageIndex{3}$

-3 (a+7)

Jibu

-3a—21

Zoezi$\PageIndex{4}$

-5 (p+9)

Zoezi$\PageIndex{5}$

2 (x-7)

Jibu

2x-14

Zoezi$\PageIndex{6}$

7 (y-4)

Zoezi$\PageIndex{7}$

—3 (k—4)

Jibu

-3k+12

Zoezi$\PageIndex{8}$

-8 (j-5)

Zoezi$\PageIndex{9}$

q (q+5)

Jibu

$q^{2}+5 q$

Zoezi$\PageIndex{10}$

(k+7)

Zoezi$\PageIndex{11}$

-b (b+9)

Jibu

$-b^{2}-9 b$

Zoezi$\PageIndex{12}$

-y (y+3)

Zoezi$\PageIndex{13}$

-x (x-10)

Jibu

$-x^{2}+10 x$

Zoezi$\PageIndex{14}$

-p (p-15)

Zoezi$\PageIndex{15}$

6r (4r+s)

Jibu

$24 r^{2}+6 r s$

Zoezi$\PageIndex{16}$

5c (9c+d)

Zoezi$\PageIndex{17}$

12x (x-10)

Jibu

$12 x^{2}-120 x$

Zoezi$\PageIndex{18}$

9m (m-11)

Zoezi$\PageIndex{19}$

-9a (3a+5)

Jibu

$-27 a^{2}-45 a$

Zoezi$\PageIndex{20}$

-4p (2p+7)

Zoezi$\PageIndex{21}$

3$\left(p^{2}+10 p+25\right)$

Jibu

$3 p^{2}+30 p+75$

Zoezi$\PageIndex{22}$

6$\left(y^{2}+8 y+16\right)$

Zoezi$\PageIndex{23}$

$-8 x\left(x^{2}+2 x-15\right)$

Jibu

$-8 x^{3}-16 x^{2}+120 x$

Zoezi$\PageIndex{24}$

$-5 t\left(t^{2}+3 t-18\right)$

Zoezi$\PageIndex{25}$

5$q^{3}\left(q^{3}-2 q+6\right)$

Jibu

$5 q^{6}-10 q^{4}+30 q^{3}$

Zoezi$\PageIndex{26}$

4$x^{3}\left(x^{4}-3 x+7\right)$

Zoezi$\PageIndex{27}$

$-8 y\left(y^{2}+2 y-15\right)$

Jibu

$-8 y^{3}-16 y^{2}+120 y$

Zoezi$\PageIndex{28}$

$-5 m\left(m^{2}+3 m-18\right)$

Zoezi$\PageIndex{29}$

5$q^{3}\left(q^{2}-2 q+6\right)$

Jibu

$5 q^{5}-10 q^{4}+30 q^{3}$

Zoezi$\PageIndex{30}$

9$r^{3}\left(r^{2}-3 r+5\right)$

Zoezi$\PageIndex{31}$

$-4 z^{2}\left(3 z^{2}+12 z-1\right)$

Jibu

$-12 z^{4}-48 z^{3}+4 z^{2}$

Zoezi$\PageIndex{32}$

$-3 x^{2}\left(7 x^{2}+10 x-1\right)$

Zoezi$\PageIndex{33}$

$(2 m-9) m$

Jibu

$2 m^{2}-9 m$

Zoezi$\PageIndex{34}$

$(8 j-1) j$

Zoezi$\PageIndex{35}$

$(w-6) \cdot 8$

Jibu

$8 w-48$

Zoezi$\PageIndex{36}$

$(k-4) \cdot 5$

Zoezi$\PageIndex{37}$

4$(x+10)$

Jibu

4x+40

Zoezi$\PageIndex{38}$

6 (y+8)

Zoezi$\PageIndex{39}$

15 (r-24)

Jibu

15r-360

Zoezi$\PageIndex{40}$

12 (mst-30)

Zoezi$\PageIndex{41}$

—3 (m+11)

Jibu

-3m-33

Zoezi$\PageIndex{42}$

-4 (p+15)

Zoezi$\PageIndex{43}$

-8 (z-5)

Jibu

-8z+40

Zoezi$\PageIndex{44}$

—3 (x-9)

Zoezi$\PageIndex{45}$

u (u+5)

Jibu

$u^{2}+5 u$

Zoezi$\PageIndex{46}$

$q(q+7)$

Zoezi$\PageIndex{47}$

$n\left(n^{2}-3 n\right)$

Jibu

$n^{3}-3 n^{2}$

Zoezi$\PageIndex{48}$

$s\left(s^{2}-6 s\right)$

Zoezi$\PageIndex{49}$

6$x(4 x+y)$

Jibu

$24 x^{2}+6 x y$

Zoezi$\PageIndex{50}$

5a (9a+b)

Zoezi$\PageIndex{51}$

5p (11p-5q)

Jibu

$55 p^{2}-25 p q$

Zoezi$\PageIndex{52}$

12$u(3 u-4 v)$

Zoezi$\PageIndex{53}$

3$\left(v^{2}+10 v+25\right)$

Jibu

$3 v^{2}+30 v+75$

Zoezi$\PageIndex{54}$

6$\left(x^{2}+8 x+16\right)$

Zoezi$\PageIndex{55}$

2$n\left(4 n^{2}-4 n+1\right)$

Jibu

$8 n^{3}-8 n^{2}+2 n$

Zoezi$\PageIndex{56}$

3$r\left(2 r^{2}-6 r+2\right)$

Zoezi$\PageIndex{57}$

$-8 y\left(y^{2}+2 y-15\right)$

Jibu

$-8 y^{3}-16 y^{2}+120 y$

Zoezi$\PageIndex{58}$

$-5 m\left(m^{2}+3 m-18\right)$

Zoezi$\PageIndex{59}$

5$q^{3}\left(q^{2}-2 q+6\right)$

Jibu

$5 q^{5}-10 q^{4}+30 q^{3}$

Zoezi$\PageIndex{60}$

9$r^{3}\left(r^{2}-3 r+5\right)$

Zoezi$\PageIndex{61}$

$-4 z^{2}\left(3 z^{2}+12 z-1\right)$

Jibu

$-12 z^{4}-48 z^{3}+4 z^{2}$

Zoezi$\PageIndex{62}$

$-3 x^{2}\left(7 x^{2}+10 x-1\right)$

Zoezi$\PageIndex{63}$

$(2 y-9) y$

Jibu

$18 y^{2}-9 y$

Zoezi$\PageIndex{64}$

$(8 b-1) b$

Kuzidisha Binomial na Binomial

Katika mazoezi yafuatayo, kuzidisha binomials zifuatazo kwa kutumia: ⓐ Mali ya Usambazaji ⓑ njia ya FOIL ⓒ Njia ya Wima.

Zoezi$\PageIndex{65}$

(w+5) (w+7)

Jibu

$w^{2}+12 w+35$

Zoezi$\PageIndex{66}$

(y+9) (y+3)

Zoezi$\PageIndex{67}$

(p+11) (p-4)

Jibu

$p^{2}+7 p-44$

Zoezi$\PageIndex{68}$

(q+4) (q-8)

Katika mazoezi yafuatayo, kuzidisha binomials. Tumia njia yoyote.

Zoezi$\PageIndex{69}$

(x+8) (x+3)

Jibu

$x^{2}+11 x+24$

Zoezi$\PageIndex{70}$

(y+7) (y+4)

Zoezi$\PageIndex{71}$

(y-6) (y-2)

Jibu

$y^{2}-8 y+12$

Zoezi$\PageIndex{72}$

(x-7) (x-2)

Zoezi$\PageIndex{73}$

(w-4) (w+7)

Jibu

$w^{2}+3 w-28$

Zoezi$\PageIndex{74}$

$(q-5)(q+8)$

Zoezi$\PageIndex{75}$

(p+12) (p-5)

Jibu

$p^{2}+7 p-60$

Zoezi$\PageIndex{76}$

(m+11) (m-4)

Zoezi$\PageIndex{77}$

(6p+5) (p+1)

Jibu

$6 p^{2}+11 p+5$

Zoezi$\PageIndex{78}$

$(7 m+1)(m+3)$

Zoezi$\PageIndex{79}$

(2t-9) (10t+1)

Jibu

$20 t^{2}-88 t-9$

Zoezi$\PageIndex{80}$

(3r-8) (11r+1)

Zoezi$\PageIndex{81}$

(5x-y) (3x-6)

Jibu

$15 x^{2}-3 x y-30 x+6 y$

Zoezi$\PageIndex{82}$

(10a-b) (3a—4)

Zoezi$\PageIndex{83}$

(a+b) (2a+3b)

Jibu

$2 a^{2}+5 a b+3 b^{2}$

Zoezi$\PageIndex{84}$

(r+s) (3r+2s)

Zoezi$\PageIndex{85}$

(4z-y) (z-6)

Jibu

$4 z^{2}-24 z-z y+6 y$

Zoezi$\PageIndex{86}$

(5x-y) (x-4)

Zoezi$\PageIndex{87}$

$\left(x^{2}+3\right)(x+2)$

Jibu

$x^{3}+2 x^{2}+3 x+6$

Zoezi$\PageIndex{88}$

$\left(y^{2}-4\right)(y+3)$

Zoezi$\PageIndex{89}$

$\left(x^{2}+8\right)\left(x^{2}-5\right)$

Jibu

$x^{4}+3 x^{2}-40$

Zoezi$\PageIndex{90}$

$\left(y^{2}-7\right)\left(y^{2}-4\right)$

Zoezi$\PageIndex{91}$

(5ab-1) (2ab+3)

Jibu

$10 a^{2} b^{2}+13 a b-3$

Zoezi$\PageIndex{92}$

(2xy+3) (3xy+2)

Zoezi$\PageIndex{93}$

(6pq-3) (4pq-5)

Jibu

$24 p^{2} q^{2}-42 p q+15$

Zoezi$\PageIndex{94}$

(3rs-7) (3rs-4)

Kuzidisha Trinomial na Binomial

Katika mazoezi yafuatayo, kuzidisha kutumia ⓐ Mali ya Usambazaji ⓑ Njia ya Wima.

Zoezi$\PageIndex{95}$

$(x+5)\left(x^{2}+4 x+3\right)$

Jibu

$x^{3}+9 x^{2}+23 x+15$

Zoezi$\PageIndex{96}$

$(u+4)\left(u^{2}+3 u+2\right)$

Zoezi$\PageIndex{97}$

$(y+8)\left(4 y^{2}+y-7\right)$

Jibu

$4 y^{3}+33 y^{2}+y-56$

Zoezi$\PageIndex{98}$

$(a+10)\left(3 a^{2}+a-5\right)$

Katika mazoezi yafuatayo, ongeze. Tumia njia yoyote.

Zoezi$\PageIndex{99}$

$(w-7)\left(w^{2}-9 w+10\right)$

Jibu

$w^{3}-16 w^{2}+73 w-70$

Zoezi$\PageIndex{100}$

$(p-4)\left(p^{2}-6 p+9\right)$

Zoezi$\PageIndex{101}$

$(3 q+1)\left(q^{2}-4 q-5\right)$

Jibu

$3 q^{3}-11 q^{2}-19 q-5$

Zoezi$\PageIndex{102}$

$(6 r+1)\left(r^{2}-7 r-9\right)$

Mazoezi ya mchanganyiko

Zoezi$\PageIndex{103}$

(10y-6) + (4y-7)

Jibu

14y-13

Zoezi$\PageIndex{104}$

(15p-4) + (3p-5)

Zoezi$\PageIndex{105}$

$\left(x^{2}-4 x-34\right)-\left(x^{2}+7 x-6\right)$

Jibu

-11x-28

Zoezi$\PageIndex{106}$

$\left(j^{2}-8 j-27\right)-\left(j^{2}+2 j-12\right)$

Zoezi$\PageIndex{107}$

5$q\left(3 q^{2}-6 q+11\right)$

Jibu

$15 q^{3}-30 q^{2}+55 q$

Zoezi$\PageIndex{108}$

8$t\left(2 t^{2}-5 t+6\right)$

Zoezi$\PageIndex{109}$

(s-7) (s+9)

Jibu

$s^{2}+2 s-63$

Zoezi$\PageIndex{110}$

(x-5) (x+13)

Zoezi$\PageIndex{111}$

$\left(y^{2}-2 y\right)(y+1)$

Jibu

$y^{3}-y^{2}-2 y$

Zoezi$\PageIndex{112}$

$\left(a^{2}-3 a\right)(4 a+5)$

Zoezi$\PageIndex{113}$

$(3 n-4)\left(n^{2}+n-7\right)$

Jibu

$3 n^{3}-n^{2}-25 n+28$

Zoezi$\PageIndex{114}$

$(6 k-1)\left(k^{2}+2 k-4\right)$

Zoezi$\PageIndex{115}$

$(7 p+10)(7 p-10)$

Jibu

$49 p^{2}-100$

Zoezi$\PageIndex{116}$

(3y+8) (3y-8)

Zoezi$\PageIndex{117}$

$\left(4 m^{2}-3 m-7\right) m^{2}$

Jibu

$4 m^{4}-3 m^{3}-7 m^{2}$

Zoezi$\PageIndex{118}$

$\left(15 c^{2}-4 c+5\right) c^{4}$

Zoezi$\PageIndex{119}$

$(5 a+7 b)(5 a+7 b)$

Jibu

$25 a^{2}+70 a b+49 b^{2}$

Zoezi$\PageIndex{120}$

(3x-11y) (3x-11y)

Zoezi$\PageIndex{121}$

(4y+12z) (4y-12z)

Jibu

$16 y^{2}-144 z^{2}$

kila siku Math

Zoezi$\PageIndex{122}$

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.

1. Panua (10+3) (10+5) kwa njia ya FOIL.
2. Panua 13·15 bila kutumia calculator.
3. Njia ipi ni rahisi kwako? Kwa nini?

Zoezi$\PageIndex{123}$

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.

1. Panua (20—2) (20-3) kwa njia ya FOIL.
2. Kuzidisha 18·17 bila kutumia calculator.
3. Njia ipi ni rahisi kwako? Kwa nini?

Jibu

1. 306
2. 306
3. Majibu yatatofautiana.

Mazoezi ya kuandika

Zoezi$\PageIndex{124}$

Ni njia gani unapendelea kutumia wakati wa kuzidisha binomials mbili: Mali ya Usambazaji, njia ya FOIL, au Njia ya Wima? Kwa nini?

Zoezi$\PageIndex{125}$

Ni njia gani unapendelea kutumia wakati wa kuzidisha trinomial kwa binomial: Mali ya Usambazaji au Njia ya Wima? Kwa nini?

Jibu

Majibu yatatofautiana.

Zoezi$\PageIndex{126}$

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.

Zoezi$\PageIndex{127}$

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.

Zoezi$\PageIndex{128}$

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.

Zoezi$\PageIndex{129}$

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?