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6 June, 02:00

Select the correct answer. What is the correct expansion of the binomial (x + y) 5? A. x5 + 5x4y + 10x3y2 + 10x3y3 + 5xy4 + y5 B. x5 + 5x4y + 10x3y2 + 10x2y3 + 5xy4 + y4 C. x5 + 5x4y + 10x3y2 + 10x2y3 + 5xy4 + y5 D. x5 + 5x4y4 + 10x3y3 + 10x2y2 + 5xy + y5

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  1. 6 June, 04:56
    0
    Answer: C

    Step-by-step explanation:

    To expand binomials there is a "newton metode"

    (X+Y) ^5 will have 6 terms (5+1)

    In the first one x is goning to be raised to the fifth power, in the esconde to the forth, and its going to decrese one by one until the last one, X^0=1

    On the other hand, Y it's going to be Y^0in the first term, and Y^5 in the 6th

    The coefficients are going to be taken from the Tartaglia triangle

    1

    1 1

    1 2 1

    1 3 3 1

    1 4 6 4 1

    1 5 10 10 5 1

    1 6 15 20 15 6 1

    It has ones on both sides and then every number is the sum of the two on it.

    Our binomial takes the coefficients of the fifth row

    Then

    We

    (X+Y) ^5 = X^5 + 5 X^4 Y + 10 X^3 Y^2 + 10 X^2 Y^3 + 5 X Y^4 + Y^5
  2. 6 June, 05:50
    0
    C. x^5 + 5x^4y + 10x^3y^2 + 10x^2y^3 + 5xy^4 + y^5

    Step-by-step explanation:

    Wrong terms are bolded:

    A. x5 + 5x4y + 10x3y2 + 10x3y3 + 5xy4 + y5

    B. x5 + 5x4y + 10x3y2 + 10x2y3 + 5xy4 + y4

    C. x5 + 5x4y + 10x3y2 + 10x2y3 + 5xy4 + y5

    D. x5 + 5x4y4 + 10x3y3 + 10x2y2 + 5xy + y5

    The sum of exponents should always be 5.
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