Answer:
1 7 21 35 35 21 7 1
Step-by-step explanation:
Pascal triangle is a mathematical expression that can be used to expand questions involving bracket, especially of high degree/ power. Example: [tex](a + b)^{9}[/tex] etc
For the given question, the Pascal triangle for the expansion is: 1 7 21 35 35 21 7 1
So that,
[tex](2x^{3}+3y^{2}) ^{7}[/tex] = 1.[tex](2x^{3}) ^{7}[/tex] + 7.[tex](2x^{3}) ^{6}[/tex].[tex]3y^{2}[/tex] + 21. [tex](2x^{3}) ^{5}[/tex].[tex](3y^{2}) ^{2}[/tex] + 35.[tex](2x^{3}) ^{4}[/tex].[tex](3y^{2}) ^{3}[/tex] + 35. [tex](2x^{3}) ^{3}[/tex].[tex](3y^{2}) ^{4}[/tex] + 21. [tex](2x^{3}) ^{2}[/tex].[tex](3y^{2})^{5}[/tex] + 7.[tex](2x^{3} )^{1}[/tex].[tex](3y^{2} )^{6}[/tex] + 1.[tex](3y^{2}) ^{7}[/tex]
= 128[tex]x^{21}[/tex] + 1344[tex]x^{18}[/tex][tex]y^{2}[/tex] + 6048[tex]x^{15}[/tex][tex]y^{4}[/tex] + 15120[tex]x^{12}[/tex][tex]y^{6}[/tex] + 22680[tex]x^{9}[/tex][tex]y^{8}[/tex] + 20412[tex]x^{6}[/tex][tex]y^{10}[/tex] + 10206[tex]x^{3}[/tex][tex]y^{12}[/tex] + 2187[tex]y^{14}[/tex]
Therefore;
[tex](2x^{3}+3y^{2}) ^{7}[/tex] = 128[tex]x^{21}[/tex] + 1344[tex]x^{18}[/tex][tex]y^{2}[/tex] + 6048[tex]x^{15}[/tex][tex]y^{4}[/tex] + 15120[tex]x^{12}[/tex][tex]y^{6}[/tex] + 22680[tex]x^{9}[/tex][tex]y^{8}[/tex] + 20412[tex]x^{6}[/tex][tex]y^{10}[/tex] + 10206[tex]x^{3}[/tex][tex]y^{12}[/tex] + 2187[tex]y^{14}[/tex]
