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Answer:
(a) a³ +21a² +147a +343
Step-by-step explanation:
The expansion of the binomial power (a +b)^n follows a pattern in which powers of 'a' decrease while powers of 'b' increase. The degree of each term is n. The coefficients of the terms are taken from the n-th row of Pascal's triangle.
For n=3, the coefficients are 1, 3, 3, 1, so the expansion is ...
(a +b)³ = a³ +3a²b +3ab² +b³
In this instance, we have a=a, and b=7, so the expansion is ...
(a +7)³ = a³ +3·a²·7 +3·a·7² +7³ = a³ +21a² +147a +343
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Comment on Pascal's triangle
The numbers at each place in the triangle are the sum of the two numbers immediately above. The left and right sides are 1; the numbers adjacent to those are the row number.
