if a+b = 8 and a² + b² = 40
then find the value of a³ + b³
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a + b= 8
a^2 + b^2 = 40
Now, a^2 + b^2 = (a + b)^2 - 2ab
40 = 82 - 2ab
2ab = 64 - 40 = 24
ab = 12
Therefore, a^3 + b^3 = (a + b)^3 - 3ab(a + b)
= 512- 3 x 12 x 8
= 512 - 288
= 224
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