How do you factor $3.375 v^{3} + 15.625 r^{6}$ $3.375v^3+15.625r^6$ ?

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How do you factor $3.375 v^{3} + 15.625 r^{6}$ $3.375v^3+15.625r^6$ ?

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Answer 1 · 2015-04-21T17:55:21

Prime factorise 3375 and 15625

3375=333555= $3^{3} \cdot 5^{3}$ $3^3*5^3$ and 15625= 555555= $5^{3} \cdot 5^{3}$ $5^3*5^3$

$3.375 v^{3} + 15.625 r^{6} = \frac{3^{3} \cdot 5^{3} \cdot v^{3}}{10^{3}} + \frac{5^{3} \cdot 5^{3}}{10^{3}} {(r^{2})}^{3}$ $3.375v^3 +15.625r^6= (3^3*5^3* v^3 )/10^3 +( 5^3*5^3)/10^3 (r^2)^3$

= $(\frac{5^{3}}{10^{3}}) [3^{3} v^{3} + 5^{3} {(r^{2})}^{3}]$ $(5^3/10^3) [3^3 v^3 +5^3 (r^2)^3]$

= $(\frac{5^{3}}{10^{3}}) [{(3 v)}^{3} + {(5 r^{2})}^{3}]$ $(5^3/10^3)[(3v)^3 +(5r^2)^3]$

= ${(\frac{5}{10})}^{3} (3 v + 5 r^{2}) (9 v^{2} - 15 v r^{2} + 25 r^{4})$ $(5/10)^3 (3v+5r^2)(9v^2 -15vr^2 +25r^4)$

= $\frac{1}{8} (3 v + 5 r^{2}) (9 v^{2} - 15 v r^{2} + 25 r^{4})$ $1/8(3v+5r^2)(9v^2 -15vr^2 +25r^4)$

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How do you factor $3.375 v^{3} + 15.625 r^{6}$ $3.375v^3+15.625r^6$ ?

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