(a+b)2=a2+b2+2ab a3+b3=(a+b)(a2+b2−ab) Calculation: First, we find the value of ab using the formula (a+b)2=a2+b2+2ab ⇒402=116+2ab ⇒1600=116+2ab ⇒1600−116=2ab ⇒1484=2ab ⇒ab= ⇒ab=742 Now, we find the value of a3+b3 using the formula a3+b3=(a+b)(a2+b2−ab) ⇒a3+b3=(40)(116−742) ⇒a3+b3=40×(−626) ⇒a3+b3=−25040