Question

If $A+B=5$ and $AB=6$. Find $A^3+B^3$.

• A. 125
• B. 90
• C. 35
• D. 215

Answer 1

The correct option is C

35

Using the identity, $(x+y{)}^3=x^3+y^3+3x^{2}y+3x{y}^2)$
$=x^3+y^3+3xy(x+y)$

This can be rewritten as $(x^3+y^3)=(x+y{)}^3-3xy(x+y)$

Substituting in A and B for x and y, we get:

$(A^3+B^3)=(A+B{)}^3-3AB(A+B)$
$=5^3-3\times 6\times 5=125-90=35$