#### Answer

$(r+2s-3t)(2r-2s+t)=2r^{2}+2rs-5rt-4s^{2}+8st-3t^{2}$

#### Work Step by Step

$(r+2s-3t)(2r-2s+t)$
Evaluate the product indicated by multiplying all three terms of the first factor by every element in the second factor separately:
$(r+2s-3t)(2r-2s+t)=...$
$...=2r^{2}-2rs+rt+4rs-4s^{2}+2st-6rt+6st-3t^{2}=...$
Simplify by combining like terms:
$...=2r^{2}+2rs-5rt-4s^{2}+8st-3t^{2}$