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3 terms multiplied by 3 terms. What are the nine pieces you get - before simplifying?
 
you know the acronym FOIL ( first outside inside last) when you have 2 terms multiplied by 2 terms? That's just a way of remembering to multiplying each term in the 1st bracket by each term in the second bracket.

(8v^2t-6vt+ 7t^2)(vt- 6t+v)

so you would have

(8v^2t)(vt)- 8v^2t(6t) + 8v^2t(v)

keep going like that
 
Hello, Ummyasmeen!

You were never taught how to multiply polynomials? . . . Hard to believe!


(8v2t6vt+7t2)(vt6t+v)\displaystyle (8v^2t-6vt+ 7t^2)(vt- 6t+v)

Simple rule: multiply each term of the 1st polynomial by each term of the 2nd polynomial.

(8v2t6vt+7t2)(vt6t+v)\displaystyle (8v^2t - 6vt + 7t^2)(vt - 6t + v)

. . =  (8v2t)(vt)+(8v2t)(-6t)+(8v2t)(v)\displaystyle =\;(8v^2t)(vt) + (8v^2t)(\text{-}6t) + (8v^2t)(v)
. . . . . . \(\displaystyle +\:(\text{-}6vt)(vt) + (\text{-}6vt)(\text{-}6t) + (\text{-}6vt)(v)\)
. . . . . . . . \(\displaystyle +\:(7t^2)(vt) + (7t^2)(\text{-}6t) +_ (7t^2)(v) \)

. . =  8v3t248v2t2+8v3t\displaystyle =\;8v^3t^2 - 48v^2t^2 + 8v^3t
. . . . . . 6v2t2+36vt26v2t\displaystyle -6v^2t^2 + 36vt^2 - 6v^2t
. . . . . . . . +7vt342t3+7vt2\displaystyle + 7vt^3 - 42t^3 + 7vt^2

. . =  8v3t2+8v3t54v2t26v2t+43vt2+7vt342t3\displaystyle =\;8v^3t^2 + 8v^3t - 54v^2t^2 - 6v^2t + 43vt^2 + 7vt^3 - 42t^3
 
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