This section is mostly instruction by example.
Adding and subtracting with exponents. Exponential terms can only be added or subtracted with other terms of the same power, or order. When these match, the co-efficients can simply be added or subtracted. Think of [katex]x^{2}+2x^{2}[/katex]. When expanded and the exponents removed, it becomes [katex]xx+2xx[/katex] which can be seen to be [katex]3xx[/katex].
Some additional examples are shown below with the first ones all being CORRECT while the second set are all INCORRECT
- Examples of CORRECT additions and subtractions:
- [katex]x^{2}+x^{2}=2x^{2}[/katex]
- [katex]2x^{3}+6x^{3}=8x^{3}[/katex]
- [katex]6y^{4}-2y^{4}=4y^{4}[/katex] — Exponents just have to be the same
- [katex]x^{2}+x^{2}+3x^{2}=5x^{2}[/katex] — We can have multiple terms
- [katex]x^{2}+x^{2}-3x^{2}=-3x^{2}[/katex] — Pay attention to the PLUS or MINUS signs
- Examples of INCORRECT additions and subtractions:
- [katex]x^{2}+x^{2}=x^{4}[/katex] — Exponents don’t add like this
- [katex]2x^{2}+6x^{3}=8x^{2}[/katex] — The exponents MUST be the same
- [katex]6y^{4}-2y^{4}=8y^{4}[/katex] — Pay attention to the PLUS or MINUS signs