SOLUTION: I need help with these two problems. Multiply (5√3-15√5) (4√3+12√5) Multiply and simplify ^3 sq rt y^4 * ^3 sq rt 16y^5

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Question 198380: I need help with these two problems.
Multiply (5√3-15√5) (4√3+12√5)
Multiply and simplify ^3 sq rt y^4 * ^3 sq rt 16y^5

Found 2 solutions by jim_thompson5910, arallie:
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
# 1



%285%2Asqrt%283%29-15%2Asqrt%285%29%29%284%2Asqrt%283%29%2B12%2Asqrt%285%29%29 Start with the given expression.


Now let's FOIL the expression.


Remember, when you FOIL an expression, you follow this procedure:


%28highlight%285%2Asqrt%283%29%29-15%2Asqrt%285%29%29%28highlight%284%2Asqrt%283%29%29%2B12%2Asqrt%285%29%29 Multiply the First terms:%285%2Asqrt%283%29%29%2A%284%2Asqrt%283%29%29=60.


%28highlight%285%2Asqrt%283%29%29-15%2Asqrt%285%29%29%284%2Asqrt%283%29%2Bhighlight%2812%2Asqrt%285%29%29%29 Multiply the Outer terms:%285%2Asqrt%283%29%29%2A%2812%2Asqrt%285%29%29=60%2Asqrt%2815%29.


%285%2Asqrt%283%29%2Bhighlight%28-15%2Asqrt%285%29%29%29%28highlight%284%2Asqrt%283%29%29%2B12%2Asqrt%285%29%29 Multiply the Inner terms:%28-15%2Asqrt%285%29%29%2A%284%2Asqrt%283%29%29=-60%2Asqrt%2815%29.


%285%2Asqrt%283%29%2Bhighlight%28-15%2Asqrt%285%29%29%29%284%2Asqrt%283%29%2Bhighlight%2812%2Asqrt%285%29%29%29 Multiply the Last terms:%28-15%2Asqrt%285%29%29%2A%2812%2Asqrt%285%29%29=-900.


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So we have the terms: 60, 60%2Asqrt%2815%29, -60%2Asqrt%2815%29, -900


60%2B60%2Asqrt%2815%29-60%2Asqrt%2815%29-900 Now add every term listed above to make a single expression.


-840 Now combine like terms.


So %285%2Asqrt%283%29-15%2Asqrt%285%29%29%284%2Asqrt%283%29%2B12%2Asqrt%285%29%29 FOILs to -840.


In other words, %285%2Asqrt%283%29-15%2Asqrt%285%29%29%284%2Asqrt%283%29%2B12%2Asqrt%285%29%29=-840.




# 2

root%283%2Cy%5E4%29%2Aroot%283%2C16y%5E5%29 Start with the given expression.


root%283%2Cy%5E4%2A16y%5E5%29 Combine the roots.


root%283%2C16y%5E9%29 Multiply


root%283%2C8%2A2%2Ay%5E9%29 Factor 16 to get 8*2


root%283%2C8%2A2%2A%28y%5E3%29%5E3%29 Rewrite y%5E9 as %28y%5E3%29%5E3


root%283%2C8%29%2Aroot%283%2C2%29%2Aroot%283%2C%28y%5E3%29%5E3%29 Break up the root.


2%2Aroot%283%2C2%29%2Aroot%283%2C%28y%5E3%29%5E3%29 Evaluate the cube root of 8 to get 2


2%2Aroot%283%2C2%29%2Ay%5E3 Evaluate the cube root of %28y%5E3%29%5E3 to get y%5E3


2y%5E3%2Aroot%283%2C2%29 Rearrange the terms.


So root%283%2Cy%5E4%29%2Aroot%283%2C16y%5E5%29=2y%5E3%2Aroot%283%2C2%29

Answer by arallie(162) About Me  (Show Source):
You can put this solution on YOUR website!
%285sqrt%283%29-15sqrt%285%29%29%284sqrt%283%29%2B12sqrt%285%29%29
%285sqrt%283%29%284sqrt%283%29%2B12sqrt%285%29%29%29-%2815sqrt%285%29%284sqrt%283%29%2B12sqrt%285%29%29%29
%2820sqrt%283%29%5E2%2B60sqrt%2815%29%29-%2860sqrt%2815%29%2B180sqrt%285%29%5E2%29
%2860%29-%28900%29=-840
Multiply and simplify ^3 sq rt y^4 * ^3 sq rt 16y^5
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