Diketahui P(x, y)=2x2−4x2y2−3xy+2y3 dan Q(x, y)=2x5+7x2y3. Tentukan P(x, y)×Q(x, y)!

Pertanyaan

Diketahui begin mathsize 14px style P open parentheses x comma space y close parentheses equals 2 x squared minus 4 x squared y squared minus 3 x y plus 2 y cubed end style dan begin mathsize 14px style Q open parentheses x comma space y close parentheses equals 2 x to the power of 5 plus 7 x squared y cubed end style. Tentukan begin mathsize 14px style P open parentheses x comma space y close parentheses cross times Q open parentheses x comma space y close parentheses end style!

A. Acfreelance

Master Teacher

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Pembahasan

Dengan menerapkan sifat distributif perkalian, diperoleh perhitungan sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell P open parentheses x comma space y close parentheses cross times Q open parentheses x comma space y close parentheses end cell row blank equals cell open parentheses 2 x squared minus 4 x squared y squared minus 3 x y plus 2 y cubed close parentheses times open parentheses 2 x to the power of 5 plus 7 x squared y cubed close parentheses end cell row blank equals cell 2 x squared times 2 x to the power of 5 plus 2 x squared times 7 x squared y cubed minus 4 x squared y squared times 2 x to the power of 5 end cell row blank blank cell negative 4 x squared y squared times 7 x squared y cubed minus 3 x y times 2 x to the power of 5 minus 3 x y times 7 x squared y cubed end cell row blank blank cell plus 2 y cubed times 2 x to the power of 5 plus 2 y cubed times 7 x squared y cubed end cell row blank equals cell 4 x to the power of 7 plus 14 x to the power of 4 y cubed minus 8 x to the power of 7 y squared minus 28 x to the power of 4 y to the power of 5 minus 6 x to the power of 6 y end cell row blank blank cell negative 21 x cubed y cubed plus 4 x to the power of 5 y cubed plus 14 x squared y to the power of 6 end cell row blank equals cell 14 x squared y to the power of 6 minus 21 x cubed y cubed plus 14 x to the power of 4 y cubed minus 28 x to the power of 4 y to the power of 5 end cell row blank blank cell plus 4 x to the power of 5 y cubed minus 6 x to the power of 6 y plus 4 x to the power of 7 minus 8 x to the power of 7 y squared end cell end table end style 

Jadi, hasil dari begin mathsize 14px style P open parentheses x comma space y close parentheses cross times Q open parentheses x comma space y close parentheses end style adalah 

begin mathsize 14px style 14 x squared y to the power of 6 minus 21 x cubed y cubed plus 14 x to the power of 4 y cubed minus 28 x to the power of 4 y to the power of 5 plus 4 x to the power of 5 y cubed minus 6 x to the power of 6 y plus 4 x to the power of 7 minus 8 x to the power of 7 y squared end style 

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