Solution to Find the expansion of a) (x + y)^6 b) (x + y)^4 31) What is … - Sikademy
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Archangel Macsika

Find the expansion of a) (x + y)^6 b) (x + y)^4 31) What is the coefficient of x^12 y^13 in the expansion of (x + y)^25? 32) What is the coefficient of x9 in (2 − x)19? 33) What is the coefficient of x^101 y^99 in the expansion of (2x − 3y)^200?

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a)


(x+y)^6=x^6+6x^5y+15x^4y^2+20x^3y^3+15x^2y^4

+6xy^5+y^6

b)


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

31)


\dbinom{25}{12}=\dfrac{25!}{12!(25-12)!}=5200300

32)


(-1)^9\dbinom{19}{10}(2)^{10}=-\dfrac{19!}{10!(19-10)!}(1024)

=-92378(1024)=-94595072

33)


(-1)^{99}\dbinom{200}{101}(2)^{101}(3)^{99}

=-\dfrac{200!}{101!(200-101)!}(2)^{101}(3)^{99}

a)


(x+y)^6=x^6+6x^5y+15x^4y^2+20x^3y^3+15x^2y^4

+6xy^5+y^6

b)


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

31)


\dbinom{25}{12}=\dfrac{25!}{12!(25-12)!}=5200300

32)


(-1)^9\dbinom{19}{10}(2)^{10}=-\dfrac{19!}{10!(19-10)!}(1024)

=-92378(1024)=-94595072

33)


(-1)^{99}\dbinom{200}{101}(2)^{101}(3)^{99}

=-\dfrac{200!}{101!(200-101)!}(2)^{101}(3)^{99}

a)


(x+y)^6=x^6+6x^5y+15x^4y^2+20x^3y^3+15x^2y^4

+6xy^5+y^6

b)


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

31)


\dbinom{25}{12}=\dfrac{25!}{12!(25-12)!}=5200300

32)


(-1)^9\dbinom{19}{10}(2)^{10}=-\dfrac{19!}{10!(19-10)!}(1024)

=-92378(1024)=-94595072

33)


(-1)^{99}\dbinom{200}{101}(2)^{101}(3)^{99}

=-\dfrac{200!}{101!(200-101)!}(2)^{101}(3)^{99}

a)


(x+y)^6=x^6+6x^5y+15x^4y^2+20x^3y^3+15x^2y^4

+6xy^5+y^6

b)


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

31)


\dbinom{25}{12}=\dfrac{25!}{12!(25-12)!}=5200300

32)


(-1)^9\dbinom{19}{10}(2)^{10}=-\dfrac{19!}{10!(19-10)!}(1024)

=-92378(1024)=-94595072

33)


(-1)^{99}\dbinom{200}{101}(2)^{101}(3)^{99}

=-\dfrac{200!}{101!(200-101)!}(2)^{101}(3)^{99}


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Question ID: mtid-5-stid-8-sqid-459-qpid-346