Expanding using binomial theorem

1. (3x - 4)^5

2. (m^2 + 2n)^4

1)

(3x - 4)^5

=5C0(3x)^5 + 5C1(3x)^4*(-4) + 5C2(3x)^3*(-4)^2 + 5C3(3x)^2*(-4)^3 + 5C4(3x)(-4)^4 + 5C5(-4)^5

= 243 x^5 - 5*(81)x^4*(4) + 10*(27)x^3*(16) - (10)*9x^2(64) + 5(3x)*(256) - 1024

= 243x^5 - 1620x^4 + 4320x^3 - 5760x^2 + 3840x - 1024

2)

(m^2 + 2n)^4

= m^8 + 8m^6 n + 24m^4 n^2 + 32mn^3 + 16n^4

243x^5, 81x^4,27x^3,9x^2,3x,1
1, -4, 16, -64, 256, -1024
(fifth row of Pascal's triangle: 1,5,10,10,5,1
now multiply the corresponding terms together, six terms in answer

m^8, m^6,m^4, m^2, 1
1, 2n, 4n^2, 8n^3, 16n^4
4th row of Pascal's triangle:1,4,6,4,1
multiply the corresponding terms together, five terms in answer