Tutor profile: Kailen T.
This equation uses the sum of cubes formula: $$a^3 + b^3 = (a+b)(a^2-ab+b^2)$$ Notice that 125 can be written as $$5^3$$ and rewrite the equation. $$x^3+5^3$$ From here, it is easy to fill in the sum of cubes formula, where $$a=x$$ and $$b=5$$, giving us our answer $$x^3 + 5^3 = (x+5)(x^2-5x+5^2)$$ (Remember the variable always goes after the term, so instead of $$x5$$ it is $$5x$$)
Describe the path of genetic information in most organisms.
Genetic information in a cell goes from DNA to RNA to protein. This question requires knowledge of the central dogma of the cell. This is a two-step process: transcription and translation. Transcription is the conversion of DNA to RNA. Think about the act of transcribing. This could be thought of as taking notes in class; simply listening to the words a teacher says and writing down these same words on a piece of paper. Ultimately, it is the same message. DNA and RNA are both strands of nucleic acids. Although there are many differences, such as DNA being double-stranded and RNA being single-stranded, these are both types of genetic information in the cell. Now translation, on the other hand, is converting RNA to protein. This can be thought of as translating your class notes into a language you do not know. Your notes still contain the same information. Although you might not understand it, someone who speaks that language does. RNA and protein are both very important pieces within a cell, but they serve completely different functions. A polymerase (a type of enzyme which synthesizes new DNA or RNA strands) would not attach itself to a protein. Among various other functions, the primary function of RNA is to serve as a messenger molecule in forming protein. Proteins can be looked at as the "workers" within a cell, completing various duties within a cell.
SImplify: $$12x^3 - 3(2x^3 + 4x -1) - 5x + 7$$
This is a simplification equation. Using PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction), we will begin with the portion of the equation in parentheses. Within the parentheses, there are no like terms. "Like terms" are terms whose variables are the same, such as $$2x$$ and $$3x$$ or $$12x^3$$ and $$20x^3$$. Therefore, you have to distribute the $$-3$$ outside of the parentheses to each of the three terms within the parentheses using multiplication (don't forget to distribute the negative sign in $$-3$$!). This gives us the new equation: $$12x^3 - 6x^3 - 12x +3 - 5x + 7$$ Now, it is time to add and/or subtract like terms, which gives us our answer: $$6x^3 - 17x +10$$
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