what is the fourth term of (x+y)^6?

Answer 1

6C3x^3y^3=20x^3y^3

Answer 2

The 6 + 1 = 7th row of Pascal's triangle is 1, 6, 15, 20, 15, 6, 1. Those are the coefficients of the terms, starting from x^6 * y^0 = x^6 and progressing through decreasing exponents of x and increasing exponents of y up to x^0 * y^6 = y^6. The fourth term uses the fourth coefficient from the list above, and an exponent for y of 4 - 1 = 3; the exponent of x is easy to find by subtraction, since the exponents must always sum to 6. The answer is 20*x^3*y^3.

Answer 3

use pascals triangle 20x^3y^3
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 5 1
1 6 15 20 15 6 1

Answer 4

Ooo my math teacher last year taught us an easy way to do this with out Pascal’s triangle or any messy equation.

I can’t really explain this well but the first term would be (6!/6!0!)(x6y0)
So the coefficient is (the power of the binomial)factorial /[(power of x)! x (power of y)! ] (so the bottom numbers add up to 6). (0!=1)

So, the 4th term would be (6!/3!3!)(x3y3) or 20x3y3

I will write out the whole thing so it is a little easier to see:

(6!/6!0!)(x6y0) + (6!/5!1!)(x5y1) + (6!/4!2!)(x4y2) + (6!/3!3!)(x3y3) + (6!/2!3!)(x2y3) + (6!/1!5!)(x1y5) + (6!/0!6!)(x0y6)

Sorry, my explanation powers have diminished over the summer. And I see yahoo does not do superscript so any number after x and y is the power of the term (obviously)

Answer 5

It is C(6;3)x^3y^3, i.e. 20x^3y^3. Look up Pascal's triangle for these kind of questions.

Answer 6

(x + y)^6

(x + y)(x + y)(x + y)(x + y)(x + y)(x + y)

(x^2 + 2xy + y^2)(x^2 + 2xy + y^2)(x^2 + 2xy + y^2)

(x^4 + 2x^3y + x^2y^2 + 2x^3y + 4x^2y^2 + 2xy^3 + x^2y^2 + 2xy^3 + y^4)(x^2 + 2xy + y^2)

(x^4 + 4x^3y + 6x^2y^2 + 4xy^3 + y^4)(x^2 + 2xy + y^2)

x^6 + 2x^5y + x^4y^2 + 4x^5y + 8x^4y^2 + 4x^3y^3 + 6x^4y^2 + 12x^3y^3 + 6x^2y^4 + 4x^3y^3 + 8x^2y^4 + 4xy^5 + x^2y^4 + 2xy^5 + y^6

x^6 + 6x^5y + 15x^4y^2 + 20x^3y^3 + 15x^2y^4 + 6xy^5 + y^6

ANS : 20x^3y^3

Answer 7

(y-x) (x+6) ^ y-x= 20x 3^y 3^y

Answer 8

Ha ha, nice try. Would you trust this answer? Stop cheating and get back to studying those formulas!

Answer 9

(a+b)^n=a^n+(nC1)(a^(n-1))b+(nC2)(a^(n-2))b^2+...+b^n

the nC1 thing is pressing n the nCr botton on scientific calculator then 1
should get 6C3(get the actual value from calculator)x^3y^3
maybe u should try it c y.

Answer 10

(x + y) * (x + y) * (x + y) * (x + y) * (x + y) * (x + y)

Do the math.