The operation of addition and subtraction can be performed on terms with similar variable. Add or subtract the coefficients on similar variable
Example:
\(10x^2 + 5x - 3x^2 + 4x\)
\(10x^2 - 3x^2 + 5x + 4x\)
\((10 - 3)x^2 + (5 + 4)x\)
\(7x^2 + 9x\)
Exponent
The exponent (such as the 2 in \( x^2\)) says how many times to use the value in a multiplication
Example:
\(2^5 = 2 \times 2 \times 2 \times 2 \times 2 = 32\)
\(a^2b = a \times a \times b\)
\(a^3b^2 = a \times a \times a \times b \times b\)
The Law on Indices
\begin{array}{cccc} \color{blue}\text{No} && \color{blue}\text{indices} &&\color{blue} \text{General Form}\\\\ 1&& a^m \times a^n && a^{m+n} \\\\ 2&&\dfrac{a^m}{a^n} && a^{m-n}\\\\ 3&&(a^m)^n &&a^{m\times n}\\\\ 4&&(a\times b)^n &&a^n \times b^n\\\\ 5&&\left(\dfrac{a}{b}\right)^n && \dfrac{a^n}{b^n}\\\\ 6&&a^{-n} && \dfrac{1}{a^n}\\\\ \end{array}
Exercise