+128474 ab =15 a^2 + b^2 =40
Note that (a + b)^4 - ( a - b)^4 = [ (a + b)^2 + ( a - b)^2 ] [ (a + b)^2 - (a - b)^2] =
[ a^2 + 2ab + b^2 + (a^2 - 2ab + b^2 ] [ ( a^2 + 2ab + b^2) - (a^2 - 2ab + b^2 ] =
[ 2a^2 + 2b^2 ] [ 4ab ] =
2 [ a^2 + b^2 ] * 4 [ ab ] =
2 [40 ] * 4 [15] =
80 * 60 =
4800
+26367 If ab = 15 and a^2 + b^2 = 40, then find (a + b)^4 - (a - b)^4.
\(\begin{array}{|rcll|} \hline (a+b)^2 &=& a^2+b^2+2ab \\ &=& 40+2*15 \\ &=& 70 \\ \mathbf{(a+b)^4} &=& \mathbf{70^2} \\\\ (a-b)^2 &=& a^2+b^2-2ab \\ &=& 40-2*15 \\ &=& 10 \\ \mathbf{(a-b)^4} &=& \mathbf{10^2} \\ \\ (a+b)^4 - (a-b)^4 &=& 70^2-10^2 \\ \mathbf{ (a+b)^4 - (a-b)^4 } &=& \mathbf{4800} \\ \hline \end{array}\)
