The numbers in Pascal’s triangle correspond to the coefficients in the expansion of binomials raised to whole-number exponents.
There are patterns in the expansions of a binomial (a +b)n:
• Each term in the expansion is the product of a number from Pascal’s triangle, a power of a, and a power of b.
• The coefficients in the expansion correspond to the numbers in the nth row in Pascal’s triangle.
• In the expansion, the exponents of a start at n and decrease by 1 down to zero, while the exponents of b start at zero and increase by 1 up to n.
• In each term, the sum of the exponents of a and b is always n.
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