Answer:
(a + b)^n = a^n + n * a^(n - 1) * b + [ n(n - 1)/2! * a^(n - 2) * b^2 ] + ..... + b^n <===let's apply :
(x+3y)^7 = x^7 + 7 * x^6 * 3y + [ (7*6/2) * x^5 * (3y)^2 ] + 7*6*5/3! * x^4 * (3y)^3 + 7*6*5*4/4! * x^3 * (3y)^4 + 7*6*5*4*3/5! * x^2 * (3y)^5 + 7*6*5*4*3*2/6! * x * (3y)^6 + 7*6*5*4*3*2*1/7! * (3y)^7
(x+3y)^7 = x^7 + 21 * x^6 * y + 21 * x^5 * 9y^2 + 7*6*5/6 * x^4 * 27y^3 + 7*6*5*4/24 * x^3 * 81y^4 + 7*6*5*4*3/120 x^2 * 243y^5 + 7*6*5*4*3*2/720 * x * 729y^6 + 1 * 2187y^7
(x+3y)^7 = x^7 + 21x^6 * y + 189 * x^5 * y^2 + 945 * x^4 * y^3 + 2835 * x^3 * y^4 + 5103 x^2 * y^5 + 5103 * x * y^6 + 2187y^7 <==== that's right, they are 8 terms.
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(2x+y)^20 = (2x)^20 + 20 * (2x)^19 * y + ... + y^20 <==== lat term is y^20
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(2x-z)^2)^6
(2x-z)^12 = (2x)^12 + 12 * (2x)^11 * -z + 12*11/2! * (2x)^10 * (-z)^2 + 12*11*10/3! * (2x)^9 * (-z)^3 + ....
fourth term : 12*11*10/3! * (2x)^9 * (-z)^3 = 220 * 512x^9 * -z^3 = -112640 * x^9 * z^3
i am not sure for this...ain't to the power of 12???
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(x+2)^5 = x^5 + 5 * x^4 * 2 + 5 * 4/2! * x^3 * 2^2 + 5 * 4 * 3/3! * x^2 * 2^3 + 5*4*3*2/4! * x * 2^4 + 5*4*3*2*1/5! * x^0 * 2^5
(x+2)^5 = x^5 + 10x^4 + 40x^3 + 80x^2 + 80x + 1 * 1 * 32
(x+2)^5 = x^5 + 10x^4 + 40x^3 + 80x^2 + 80x + 32 <===Answer and there is a missing term in the given options.
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(3x + 2y)^5 = (3x)^5 + 5 * (3x)^4 * 2y + 5*4/2! * (3x)^3 * (2y)^2 + ....
(3x + 2y)^5 = 243x^5 + 810x^4 * y + 1080x^3 * y^2 + ....
Step-by-step explanation:
