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

Answer:

$4034.40

step-by-step explanation:

the perimeter of the field is the sum of the lengths of the four sides:

47 yd + 158 yd + 47 yd + 158 yd = 410 yd

the cost of 3 ft (1 yd) of fence is 3×$3.28 = $9.84.

so the cost of jake's wood perimeter fance is

(410 yd) × ($9.84 /yd) = $4034.40