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

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Answer 1 · 2018-04-21T16:31:17

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

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!

Answer 2 · 2018-04-21T18:00:04

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

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#.