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Binomial Theorem Coefficients

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StarStarStarStar

Expansion of (x+y)2(x+y)^2

StarStarStarStar

1x2+2xy+1y21x^2 + 2xy + 1y^2

StarStarStarStar

Expansion of (x+y)10(x+y)^{10}

StarStarStarStar

1x10+10x9y+45x8y2+120x7y3+210x6y4+252x5y5+210x4y6+120x3y7+45x2y8+10xy9+1y101x^{10} + 10x^9y + 45x^8y^2 + 120x^7y^3 + 210x^6y^4 + 252x^5y^5 + 210x^4y^6 + 120x^3y^7 + 45x^2y^8 + 10xy^9 + 1y^{10}

StarStarStarStar

Expansion of (x+y)7(x+y)^7

StarStarStarStar

1x7+7x6y+21x5y2+35x4y3+35x3y4+21x2y5+7xy6+1y71x^7 + 7x^6y + 21x^5y^2 + 35x^4y^3 + 35x^3y^4 + 21x^2y^5 + 7xy^6 + 1y^7

StarStarStarStar

Expansion of (x+y)5(x+y)^5

StarStarStarStar

1x5+5x4y+10x3y2+10x2y3+5xy4+1y51x^5 + 5x^4y + 10x^3y^2 + 10x^2y^3 + 5xy^4 + 1y^5

StarStarStarStar

Expansion of (x+y)4(x+y)^4

StarStarStarStar

1x4+4x3y+6x2y2+4xy3+1y41x^4 + 4x^3y + 6x^2y^2 + 4xy^3 + 1y^4

StarStarStarStar

Expansion of (x+y)3(x+y)^3

StarStarStarStar

1x3+3x2y+3xy2+1y31x^3 + 3x^2y + 3xy^2 + 1y^3

StarStarStarStar

Expansion of (x+y)8(x+y)^8

StarStarStarStar

1x8+8x7y+28x6y2+56x5y3+70x4y4+56x3y5+28x2y6+8xy7+1y81x^8 + 8x^7y + 28x^6y^2 + 56x^5y^3 + 70x^4y^4 + 56x^3y^5 + 28x^2y^6 + 8xy^7 + 1y^8

StarStarStarStar

Expansion of (x+y)11(x+y)^{11}

StarStarStarStar

1x11+11x10y+55x9y2+165x8y3+330x7y4+462x6y5+462x5y6+330x4y7+165x3y8+55x2y9+11xy10+1y111x^{11} + 11x^{10}y + 55x^9y^2 + 165x^8y^3 + 330x^7y^4 + 462x^6y^5 + 462x^5y^6 + 330x^4y^7 + 165x^3y^8 + 55x^2y^9 + 11xy^{10} + 1y^{11}

StarStarStarStar

Expansion of (x+y)6(x+y)^6

StarStarStarStar

1x6+6x5y+15x4y2+20x3y3+15x2y4+6xy5+1y61x^6 + 6x^5y + 15x^4y^2 + 20x^3y^3 + 15x^2y^4 + 6xy^5 + 1y^6

StarStarStarStar

Expansion of (x+y)9(x+y)^9

StarStarStarStar

1x9+9x8y+36x7y2+84x6y3+126x5y4+126x4y5+84x3y6+36x2y7+9xy8+1y91x^9 + 9x^8y + 36x^7y^2 + 84x^6y^3 + 126x^5y^4 + 126x^4y^5 + 84x^3y^6 + 36x^2y^7 + 9xy^8 + 1y^9

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