Bob has a marble. The marble has a mass of 10g and a volume of 2cm3. What is the marble's density?

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pcastaneda03

02.08.2020

Mathematics

$\bf \textit{difference of squares}
\\ \quad \\
(a-b)(a+b) = a^2-b^2\qquad \qquad 
a^2-b^2 = (a-b)(a+b)\\\\
-----------------------------\\\\
4x^4-324\implies 4[x^4-81]\quad 
\begin{cases}
x^4\to x\cdot x\cdot x\cdot x\\
\qquad x^2\cdot x^2\\
\qquad (x^2)^2\\\\
81\to 3\cdot 3\cdot 3\cdot 3\\
\qquad 3^2\cdot 3^2\\
\qquad (3^2)^2
\end{cases}
\\\\\\
4[(x^2)^2-(3^2)^2]\implies 4[\ \underline{x^2-3^2}\ ][\ x^2+3^2\ ]
\\\\\\
4[\ \underline{(x-3)(x+3)}\ ][\ x^2+3^2\ ]
\\\\\\
4(x-3)(x+3)(x^2+9)$

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