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

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

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.