RUMUS


RUMUS-RUMUS ALJABAR
1. EKSPONEN (PANGKAT)
1.a.a^{p}xa^{q} = a^{p+q}
1.b.\frac {a^{p}}{a^{q}} = a^{p-q}
1.c.(a^{p})^{q} = a^{pq}
1.d.(a.b)^{p} = a^{p}.b^{p}
1.e.\left( \frac {a}{b} \right )^{p} = \frac {a^{p}}{b^{p}} ,  b \ne 0
1.f.a^{0} = 1
1.g. a^{-1} = \frac {1}{a^p} , a \ne 0
1.h. a^{ \frac {m}{n}} =  \sqrt[n]{a^{m}}
2. BENTUK AKAR
2.a. m \sqrt{a} + n \sqrt{a} = (m+n) \sqrt{a}
2.b.m \sqrt{a} - n \sqrt{a} = (m-n) \sqrt{a}
2.c.m \sqrt{a} . n \sqrt{b} = mn \sqrt{ab}
2.d.\left( \sqrt [n]{a} \right)^{n} = a
2.e.\sqrt [n]{ab} = \sqrt [n]{a}. \sqrt [n]{b}
2.f. \sqrt [m]{\sqrt [n]{a}} = \sqrt [mn]{a}
2.g. \sqrt [n]{\frac {a}{b}} = \frac {\sqrt [n]{a}}{\sqrt [n]{b}}
2.h. \sqrt{(a+b) + 2 \sqrt {ab}} = \sqrt {a} + \sqrt {b}
2.i. \sqrt{(a+b) - 2 \sqrt {ab}} = \sqrt {a} - \sqrt {b} untuk a > b.

3. rumus rumus lain
3.a. (a+b)^{2} = a^{2} + 2ab + b^{2}
3.b.(a-b)^{2} = a^{2} - 2ab + b^{2}
3.c.(a+b)(a-b) = a^{2} - b^{2}
3.d. (a+b)^{3} = a^{3} + 3a^{2}b + 3ab^{2} + b^{3}
3.e. (a-b)^{3} = a^{3} - 3a^{2}b + 3ab^{2} - b^{3}
3.f. a^{3} - b^{3} = (a-b)(a^{2} + ab + b^{2} )
3.g. a^{3}+b^{3} =(a+b) (a^{2} - ab + b^{2}
3.h. (a+b)^{n}=a^{n}+nC_{1}a^{n-1}b+nC_{2}a^{n-2}b^{2}+nC_{3}a^{n-3}b^{3}+....
\hspace{15 mm}+nC_{r}a^{n-r}b^{r}+.....+b^{n} \hspace{5mm}, jika n bilangan positif
dimana nCr = \frac{n!}{(n-r)!.r!}
dan n! = n.(n-1).(n-2).(n-3)....3.2.1
4. Persamaan kuadrat.I

2 thoughts on “RUMUS

  1. hebat pak……
    itu akan banyak membantu siswa sma sederajad yang membutuhkan rumus2, soal2 ataupun bahan lainnya untuk menghadapi UN…. semangat terus….
    semangat..semangat…semangat..

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