Question:
If \[ a-b=6 \quad \text{and} \quad ab=20 \] find:
\[ a^3-b^3 \]
Solution:
Using identity:
\[ a^3-b^3=(a-b)^3+3ab(a-b) \]
Substituting the given values:
\[ a^3-b^3=(6)^3+3(20)(6) \]
\[ =216+360 \]
\[ =576 \]
If \[ a-b=6 \quad \text{and} \quad ab=20 \] find:
\[ a^3-b^3 \]
Using identity:
\[ a^3-b^3=(a-b)^3+3ab(a-b) \]
Substituting the given values:
\[ a^3-b^3=(6)^3+3(20)(6) \]
\[ =216+360 \]
\[ =576 \]