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Question 415037: (a^2+5ab+6b^2/a^2-5ab+6b^2) * (10a-30b/5a+10b)
Answer by woolybear(13)   (Show Source):
You can put this solution on YOUR website! If simplify this what you come up with.
(a^(2)+5ab+(6b^(2))/(a^(2))-5ab+6b^(2))*(10a-(30b)/(5)*a+10b)
Since 5ab and -5ab are like terms, add -5ab to 5ab to get 0.
(a^(2)+(6b^(2))/(a^(2))+6b^(2))*(10a-(30b)/(5)*a+10b)
To add fractions, the denominators must be equal. The denominators can be made equal by finding the least common denominator (LCD). In this case, the LCD is a^(2). Next, multiply each fraction by a factor of 1 that will create the LCD in each of the fractions.
(a^(2)*(a^(2))/(a^(2))+(6b^(2))/(a^(2))+6b^(2)*(a^(2))/(a^(2)))*(10a-(30b)/(5)*a+10b)
Complete the multiplication to produce a denominator of a^(2) in each expression.
((a^(4))/(a^(2))+(6b^(2))/(a^(2))+(6a^(2)b^(2))/(a^(2)))*(10a-(30b)/(5)*a+10b)
Combine the numerators of all expressions that have common denominators.
((a^(4)+6b^(2)+6a^(2)b^(2))/(a^(2)))*(10a-(30b)/(5)*a+10b)
Reorder the polynomial a^(4)+6b^(2)+6a^(2)b^(2) alphabetically from left to right, starting with the highest order term.
((a^(4)+6a^(2)b^(2)+6b^(2))/(a^(2)))*(10a-(30b)/(5)*a+10b)
Reduce the expression -(30b)/(5) by removing a factor of 5 from the numerator and denominator.
((a^(4)+6a^(2)b^(2)+6b^(2))/(a^(2)))*(10a-6b*a+10b)
Multiply -6b by a to get -6ab.
((a^(4)+6a^(2)b^(2)+6b^(2))/(a^(2)))*(10a-6ab+10b)
Reorder the polynomial 10a-6ab+10b alphabetically from left to right, starting with the highest order term.
((a^(4)+6a^(2)b^(2)+6b^(2))/(a^(2)))*(-6ab+10a+10b)
Multiply each term in the first polynomial by each term in the second polynomial.
((a^(4)+6a^(2)b^(2)+6b^(2))/(a^(2))*-6ab+(a^(4)+6a^(2)b^(2)+6b^(2))/(a^(2))*10a+(a^(4)+6a^(2)b^(2)+6b^(2))/(a^(2))*10b)
Multiply ((a^(4)+6a^(2)b^(2)+6b^(2)))/(a^(2)) by each term in -6ab+10a+10b to get -(2(3a^(5)b+18a^(3)b^(3)-5a^(5)-30a^(3)b^(2)-5a^(4)b-30a^(2)b^(3)+18ab^(3)-30ab^(2)-30b^(3)))/(a^(2)).
(-(2(3a^(5)b+18a^(3)b^(3)-5a^(5)-30a^(3)b^(2)-5a^(4)b-30a^(2)b^(3)+18ab^(3)-30ab^(2)-30b^(3)))/(a^(2)))
Remove the parentheses around the expression -(2(3a^(5)b+18a^(3)b^(3)-5a^(5)-30a^(3)b^(2)-5a^(4)b-30a^(2)b^(3)+18ab^(3)-30ab^(2)-30b^(3)))/(a^(2)).
-(2(3a^(5)b+18a^(3)b^(3)-5a^(5)-30a^(3)b^(2)-5a^(4)b-30a^(2)b^(3)+18ab^(3)-30ab^(2)-30b^(3)))/(a^(2))
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