Question

Verify:- (a+b)³=a³+3a²b+3ab+b³
Army's please help​

Answer 1

Volume of Arrangement 1

Volume of the stack in Figure 6.1 = (a+b)³.

volume of Arrangement 1 of the cubes =(a+b)³.

Volume of Arrangement 2

Volume of Stack I [stack in Figure 6.2(a)] = a³.

Volume of each of Stacks II, III and IV = a²b.

total volume of the three stacks [shown in Figure 6.2(b)] = 3a²b.

Volume of each of Stacks V, VI and VII = ab².

total volume of the three stacks [shown in Figure 6.2(c)] = 3ab².

Volume of Stack VIII =b³.

Thus, total volume of Arrangement 2 of the cubes = a³ + 3a²b + 3ab² +b³.

Since the total volume in the two arrangements must be the same,

therefore

(a+b)³ =a³ + 3a²b + 3ab² +b³.

Result

It is verified that (a+b)³ =a³ + 3a²b + 3ab² +b³.