Adadin cubes da su bambancin: acronym Formula multiplication

LISSAFI - shi ne daya daga cikin wadanda sciences da suke da muhimmanci ga da wanzuwar mutãne. Kusan kowace mataki, kowane tsari ya shafi yin amfani da ilmin lissafi da kuma ta ainihin yadda ake gudanar. Mutane da yawa mai girma masana kimiyya sun yi gagarumin} o} arin tabbatar da cewa kimiyya yin wannan sauki kuma mafi ilhama. Daban-daban theorems da dabarbari axiom zai taimaka dalibai samun da bayanai da kuma amfani da ilimi. Mafi yawan su suna tuna dukan rayuwarsa.

A mafi yawan dace dabara da damar dalibai da kuma daliban mu jimre wa da babbar misalai, kasarun adadi, m da m maganganu ne dabarbari, ciki har da nata multiplication:

1. A Naira Miliyan Xari da bambanci na cubes :

s ³ - t ³ - bambanci.

k + l ^{3 3} - jimla.

2. A Naira Miliyan Xari da shigen sukari dabara, kazalika da bambanci tsakanin shigen sukari:

(F + g) da kuma ³ (h - d) ^3.

3. A bambanci na murabba'ai:

z ² - v ^2;

4. The square da Miliyan Xari:

(N + m) ² da t. D.

Da dabara ne Naira Miliyan Xari da cubes ne kusan wuya sosai haddace da wasa. Wannan tushe daga alternating ãyõyi a dikodi mai. Rubuta su kuskure, rudani zuwa wasu dabarbari.

A Naira Miliyan Xari da cubes aka bayyana kamar haka:

³ k + l ³ = (k + l) * (k ² - k * l + l ^2).

A kashi na biyu na lissafi ne wani lokacin rude tare da wani quadratic lissafi ko magana ya bayyana adadin da square da aka kara wa wa'adi na biyu, wato, to «k * l» yawan 2. Duk da haka, da dabara adadin cubes bayyana ne kawai hanya. Bari mu tabbatar da daidaici da dama da kuma gefen hagu.

Zo baya, Ina nufin, ƙoƙari nuna cewa na biyu rabin (k + l) * (k ² - k * l + l ²⁾ zai zama daidai da magana k + l ^{3 3.}

Mu cire parentheses, ya riɓaɓɓanya sharuddan. Don yin wannan, na farko ninka «k» ga kowane memba na biyu magana:

k * (k ² - k * l + k ²⁾ = k * l ² - k * (k * l) + k * (l ^2);

sa'an nan a cikin hanya kayan aiki da wani ba a sani ba «l»:

l * (k ² - k * l + k ²⁾ = l * k ² - l * (k * l) + l * (l ^2);

simplifying sakamakon magana da dabara adadin cubes, bayyanãwa Katakon, kuma a lokaci guda ba kama sharuddan:

(K ³ - k ² * l + k * l ²⁾ + (l * k ² - l ² * k + l ³ ) = K ³ - k ² l + kl ^{2 2} + lk - Luka ² + l ³ = k ³ - k ² l + k ² l + kl ² - kl ² + l ³ = k ³ + l ^3.

Wannan magana ne daidaita da asali version na dabara adadin cubes, kuma shi ne da za a nuna.

Mun sami shaida ga magana daga s ³ - t ^3. Wannan ilmin lissafi dabara na nata multiplication da ake kira da bambanci na cubes. an saukar da shi a matsayin haka:

s ³ - t ³ = (s - t) * (s ² + t * s + t ^2).

Hakazalika kamar yadda a baya misali tabbatar da iri matching da dama da hagu sassa. Don yin wannan, cire parentheses, ya riɓaɓɓanya sharuddan:

ga wani ba a sani ba «s»:

s * (s ² + s * t + t ²⁾ = (s ² + s ³ t + st ^2);

ga wani ba a sani ba «t»:

t * (s ² + s * t + t ²⁾ = (s ² t + st ² + t ^3);

hira da baka bayyana wannan bambanci an samu:

s ³ + s ^{2 2} t + st - s ² t - s ² t - t ³ = s ³ + s ² t- s ² t - st + st ^{2 2} - t ³ = s ³ - t ³ - kamar yadda ake bukata tabbatar.

Don tuna da haruffa an sanya kan fadada wannan magana, shi wajibi ne don kula da ãyõyin tsakanin sharuddan. Saboda haka, idan daya ba a sani ba ne rabu wani ilmin lissafi alama ce "-", sa'an nan a cikin na farko sashi zai zama korau, da kuma na biyu - biyu-da. Idan dake tsakanin cubes alamar "+", sa'an nan, bi da bi, wani na farko multiplier zai dauki kashi da kuma debe biyu, sa'an nan kuma da.

Wannan za a iya wakilta a cikin hanyar kananan makircinsu:

s ³ - t ³ → ( «debe") * ( "da" "da");

k + l ^{3 3} → ( "da") * ( "debe" "da").

Ka yi la'akari da wannan misali:

Ganin magana (w - 2) + ³ 8. Ya kamata bude baka.

bayani:

(W - 2) + ³ 8 za a iya wakilta (w - 2) + ³ 2 ³

Haka kuma, kamar yadda Naira Miliyan Xari da cubes, wannan magana za a iya fadada bisa ga dabara da nata multiplication:

(W - 2 + 2) * ((w - 2) ² - 2 * (w - 2) 2 + ^2);

Sa'an nan rage wuya da magana:

w * (w ² - 4w + 4 - 2w + 4 + 4) = w * (w ² - 6w + 12) = w ³ - 6w ² + 12w.

A wannan yanayin, kashi na farko (w - 2) ³ kuma za a iya daukarsa a matsayin wani shigen sukari bambanci:

(H - d) = h ^{3 3} - 3 * h ² * d + 3 * h * d ² - d ^3.

Sa'an nan kuma, idan ka bude shi a kan wannan dabara, ka samu:

(W - 2) ³ = w ³ - 3 * w ² * 2 + 3 * 2 * w ² - 2 ³ = w ³ - 6 * w ² + 12w - 8.

Idan muka ƙara wa shi kashi na biyu na asali misalai, wato, "8", sakamakon ne kamar haka:

(W - 2) + 8 = ³ w ³ - 3 * w ² * 2 + 3 * 2 * w ² - 2 ³ + 8 = w ³ - 6 * w ² + 12w.

Saboda haka, mun samu wani bayani na wannan misali a cikin hanyoyi biyu.

Yana dole ne a tuna da cewa key ga nasara a wani kasuwanci, ciki har da a warware ilmin lissafi misalai ne juriyarsu da kuma kula.