Question

Use Pascal's triangle or the Binomial theorem to expand the binomials.
1. (3c-2d)^4
2. (2n+3)^5
3. (x^2+4)^3

Answer 1

$(3c-2d)^4=(3c)^4-4(3c)^3\cdot2d+6\cdot(3c)^2\cdot(2d)^2-4\cdot3c\cdot(2d)^3-(2d)^4\\\\=81c^4-216c^3d+216c^2d^2-96cd^3-16d^4\\-------------------------------\\(2n+3)^2\\=(2n)^5+5(2n)^4\cdot3+10(2n)^3\cdot3^2+10(2n)^2\cdot3^3+5\cdot2n\cdot3^4+3^5\\\\=32n^5+240n^4+720n^3+1080n^2+810n+243\\-------------------------------\\(x^2+4)^3=(x^2)^3+3(x^2)^2\cdot4+3x^2\cdot4^2+4^3\\\\=x^6+12x^4+48x^2+64$