If a+b=5 and a*b=2 what is a^3+b^3=?

95



Explanation:

Use the sum of cubes factoring rule to get
a^3 + b^3 = (a+b)*(a^2-a*b+b^2)

On the right hand side of the equation, we can see the basic elements of: a, b, a^2, a*b, and b^2

We know that a+b = 5, which squares out to
(a+b)^2 = 5^2
a^2+2ab+b^2 = 25
a^2+2*(ab)+b^2 = 25
a^2+2*(2)+b^2 = 25 <<--- replaced ab with 2 (since a*b = 2)
a^2+4+b^2 = 25
a^2+b^2 = 25-4
a^2+b^2 = 21

That equation will help us find the answer. We don't know that a^2 or b^2 are individually, but we know combined they are equal to 21. Similarly the same goes for 'a' and 'b' as well. We don't know either 'a' nor 'b', but we know that a+b = 5

Let's use this to find the answer
a^3 + b^3 = (a+b)*(a^2-a*b+b^2)
a^3 + b^3 = (a+b)*(a^2+b^2-a*b)
a^3 + b^3 = (5)*(21-2)
a^3 + b^3 = (5)*(19)
a^3 + b^3 = 95 which is the answer

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