something to do with pascal??

Algebra Level 3

Simplify the expression: $(x-1)^4 +4(x-1)^3+6(x-1)^2+4(x-1)+1$ .

x^4

x^2-1

x^3 + 1

x^4-1

1 solution

Rowegie Lambojon
Jan 5, 2015

let x-1 = a.

then substitute: a^{4} + 4 (a^{3}) + 6(a^{2}) + 4(a)+ 1 . then the expression above can be simplified into (a + 1)^{4}. then substitute x-1.

so, ( (x-1) + 1)^{4}= x^{4}