Question 1052041
What would {{{ (4sqrt( 3) - 2sqrt (5) ) }}} be multiplied by to get {{{ (4sqrt (3) )^3 - (2sqrt (5) )^3 }}}?
<pre>Difference of cubes binomial {{{a^3 - b^3)}}} is factored as: {{{(a - b)(a^2 + ab + b^2)}}}
Likewise, {{{(4sqrt(3))^3 - (2sqrt(5))^3}}} is factored as: {{{(4sqrt(3) - 2sqrt(5))((4sqrt(3))^2 + 4sqrt(3) * 2sqrt(5) + (2sqrt(5))^2)}}}______{{{(4sqrt(3) - 2sqrt(5))(48 + 8sqrt(15) + 20)}}}_____{{{(4sqrt(3) - 2sqrt(5))(68 + 8sqrt(15))}}}
Therefore, {{{(4sqrt(3) - 2sqrt(5))}}} is MULTIPLIED by {{{highlight_green(matrix(1,5, (4sqrt(3))^2 + 4sqrt(3) * 2sqrt(5) + (2sqrt(5))^2, or, (4sqrt(3))^2 + 8sqrt(15) + (2sqrt(5))^2, or, 68 + 8sqrt(15)))}}} to get: {{{(4sqrt(3))^3 - (2sqrt(5))^3}}}