(x+1)(x+2)(x+3)(x+4)-4 ?

2 Answers
Apr 21, 2018

x^4 + 10x^3 + 35x^2 + 50x + 20

Explanation:

Use the Distributive Property:

(x+1)(x+2)(x+3)(x+4)-4
x^4 + 6x^3 + 11x^2 + 6x + 4x^3 + 24x^2 + 44x +24 - 4

Combine Like Terms:

x^4 + 6x^3 + 11x^2 + 6x + 4x^3 + 24x^2 + 44x +24 - 4
x^4 + 10x^3 + 35x^2 + 50x + 20

There's your answer!

Apr 21, 2018

x^4+10x^3+35x^2+50x+20.

Explanation:

Let, p(x)=(x+1)(x+2)(x+3)(x+4)-4,

={(x+1)(x+4)}{(x+2)(x+3)}-4,

={x^2+4x+x+4}{x^2+3x+2x+6}-4,

=(x^2+5x+4)(x^2+5x+6)-4,

=(y+4)(y+6)-4...........[y=x^2+5x],

=(y^2+6y+4y+24)-4,

=y^2+10y+20

=(x^2+5x)^2+10(x^2+5x)+20...[because, y=x^2+5x]

=(x^4+10x^3+25x^2)+(10x^2+50x)+20,

rArr p(x)=x^4+10x^3+35x^2+50x+20.