SOLUTION: For x²(a-b)+a²(b-x)+b²(x-a) show that (x-a) is a linear factor.
PLEASE HELP ME!!!!!!
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Question 166513: For x²(a-b)+a²(b-x)+b²(x-a) show that (x-a) is a linear factor.
PLEASE HELP ME!!!!!!
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
For x²(a-b)+ a²(b-x)+ b²(x-a) show that (x-a) is a linear factor.
:
Multiply to eliminate the brackets, we can leave the last term alone
x^2a - x^2b + a^2b - xa^2 + b^2(x-a)
:
Regroup:
x^2a - xa^2 + a^2b - x^2b + b^2(x-a)
:
Factor out xa and b
xa(x-a) + b(a^2 - x^2) + b^2(x-a)
:
Change the sign of b to -, to change signs inside the brackets
xa(x-a) - b(x^2 - b^2) + b^2(x-a)
:
Note that x^2 - b^2 is the "difference of squares and can be factored
xa(x-a) - b(x-a)(x+a) + b^2(x-a)
:
Note that each term contains the factor (x-a) now
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