# Aljabar Dasar

### Operasi Aljabar

###### Penjumlahan dan Pengurangan

Operasi penjumlahan dan pengurangan dapat dilakukan pada suku-suku dengan variabel yang sama.

Contoh 01

\begin{equation*} \begin{split} & 5a - 9b - 3c + 2a + 7b + 6c \\\\ & 5a + 2a - 9b + 7b - 3c + 6c \\\\ & 7a - 2b + 3c \end{split} \end{equation*}

Contoh 02

\begin{equation*} \begin{split} & 3x^2 + 6x - 5 - x^2 - 2x + 1 \\\\ & 3x^2 - x^2 + 6x - 2x - 5 + 1 \\\\ & 2x^2 + 4x - 4 \end{split} \end{equation*}

###### Perkalian dan Pembagian

Contoh 01

$$2ab\times (-3ac) \times (-4c)$$

\begin{equation*} \begin{split} &2 \:.\: (-3) \:.\: (-4) \times a \:.\: a \times b \times c \:.\: c \\\\ &24 \: a^2 \: b \: c^2 \end{split} \end{equation*}

Contoh 02

$$\dfrac{12 \: m^2 \: p^4}{14 \: m^3 \: p^3}\times \dfrac{7 \: m^4 \: p^2}{3 \: m \: p^3}$$

\begin{equation*} \begin{split} & \frac {12 \:.\: 7}{14 \:.\: 3} \times \frac {m^2 \:.\: m^4}{m^3 \:.\: m} \times \frac {p^4 \;.\: p^2}{p^3 \:.\: p^3} \\\\ & \frac {\cancelto {4} {12} \:.\: \cancel{7}}{\cancelto {2} {14} \:.\: \cancel{3}} \times \frac {m^6}{m^4} \times \frac {p^6}{p^6} \\\\ & 2 \:.\: m^2 \end{split} \end{equation*}

Contoh 03

$$(-3 \: x \: y^2)^3$$

\begin{equation*} \begin{split} &(-3)^3 \:.\: x^3  \:.\: y^6 \\\\ &-27 \:.\: x^3 \:.\: y^6 \end{split} \end{equation*}

Contoh 04

$$(7x + 3y)(5x - 2y)$$

\begin{equation*} \begin{split} & 7x \:.\: 5x + 7x \:.\: -2y + 3y \:.\: 5x + 3y \:.\: -2y \\\\ & 35x^2 - 14xy + 15 xy - 6y^2 \\\\ & 35x^2 + xy - 6y^2 \end{split} \end{equation*}

###### Faktorisasi

Contoh 01

Faktorkan $$20 + 10x$$

$$20 + 10x = 10(2 + x)$$

Contoh 02

Faktorkan $$21ab - 14bc$$

$$(21ab - 14bc = 7b(3a - 2c)$$

Contoh 03

$$2a(p-q) - 5(p-q)$$

$$2a(p-q) - 5(p-q) = (p-q)(2a - 5)$$

##### SOAL LATIHAN

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