Question

PLEASE ANSWER! I’m a tad desperate..

Answer 1

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: $(a + b)^{9}$ etc

For the given question, the Pascal triangle for the expansion is: 1 7 21 35 35 21 7 1

So that,

$(2x^{3}+3y^{2}) ^{7}$ = 1.$(2x^{3}) ^{7}$ + 7.$(2x^{3}) ^{6}$.$3y^{2}$  + 21. $(2x^{3}) ^{5}$.$(3y^{2}) ^{2}$ + 35.$(2x^{3}) ^{4}$.$(3y^{2}) ^{3}$ + 35. $(2x^{3}) ^{3}$.$(3y^{2}) ^{4}$ + 21. $(2x^{3}) ^{2}$.$(3y^{2})^{5}$ + 7.$(2x^{3} )^{1}$.$(3y^{2} )^{6}$ + 1.$(3y^{2}) ^{7}$

   = 128$x^{21}$ + 1344$x^{18}$$y^{2}$ +  6048$x^{15}$$y^{4}$ + 15120$x^{12}$$y^{6}$ + 22680$x^{9}$$y^{8}$ + 20412$x^{6}$$y^{10}$ + 10206$x^{3}$$y^{12}$ + 2187$y^{14}$

Therefore;

$(2x^{3}+3y^{2}) ^{7}$ = 128$x^{21}$ + 1344$x^{18}$$y^{2}$ +  6048$x^{15}$$y^{4}$ + 15120$x^{12}$$y^{6}$ + 22680$x^{9}$$y^{8}$ + 20412$x^{6}$$y^{10}$ + 10206$x^{3}$$y^{12}$ + 2187$y^{14}$