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Question

How are Pascal’s triangle and binomial expansion such as left parenthesis a plus b right parenthesis to the power of 5 related?

The correct answer is: Here, the coefficients of the expansions are the elements of the sixth row of the Pascal’s triangle.


    ANSWER:
    Hint:
    Pascal's Triangle gives us the coefficients for an expanded binomial of the form (a + b)n, where n is the row of the triangle. The Binomial Theorem tells us we can use these coefficients to find the entire expanded binomial, with a couple extra tricks thrown in.
    Step 1 of 1:

    Pascal's Triangle is a method to know the binomial coefficients of terms of binomial expression (x + y)n, where n can be any positive integer and x,y are real numbers. Pascal Triangle is represented in a triangular form, it is kind of a number pattern in the form of a triangular arrangement.
    The binomial expansion of left parenthesis a plus b right parenthesis to the power of 5 is:
    left parenthesis a plus b right parenthesis to the power of 5 equals 5 C subscript 0 a to the power of 5 plus 5 C subscript 1 left parenthesis a right parenthesis to the power of 4 left parenthesis b right parenthesis plus 5 C subscript 2 left parenthesis a right parenthesis cubed left parenthesis b right parenthesis squared plus 5 C subscript 3 left parenthesis a right parenthesis squared left parenthesis b right parenthesis cubed plus 5 C subscript 4 left parenthesis a right parenthesis left parenthesis b right parenthesis to the power of 4 plus 5 C subscript 5 left parenthesis b right parenthesis to the power of 5
    equals a to the power of 5 plus 5 a to the power of 4 b plus 10 a cubed b squared plus 10 a squared b cubed plus 5 a b to the power of 4 plus b to the power of 5
    Here, the coefficients of the expansions are the elements of the sixth row of the Pascal’s triangle.
    Note:
    You can find the expansion of  left parenthesis x plus y right parenthesis to the power of nusing both Pascal’s triangle and binomial expansion

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