Question

\((x + 2) (x + 3) (x + 4) (x + 5) - 8\)

Answer 1

`(x+2)(x+3)(x+4)(x+5)-8`

`=[(x+2)(x+5)][(x+3)(x+4)]-8`

`=(x^2 +7x+10)(x^2 +7x+12)-8`

`=(x^2 +7x+10)^2 +2(x^2 +7x+10)-8`

`=(x^2 +7x+10)^2 +4(x^2 +7x+10)-2(x^2 +7x+10)-8`

`=(x^2 +7x+10)(x^2 +7x+10+4)-2(x^2 +7x+10+4)`

`=(x^2 +7x+10-2)(x^2 +7x+10+4)`

`=(x^2 +7x+8)(x^2 +7x+14)`

Answer 2

\(=\left(x^2+7x+10\right)\left(x^2+7x+12\right)-8\)

\(=\left(x^2+7x\right)^2+22\left(x^2+7x\right)+112\)

\(=\left(x^2+7x+8\right)\left(x^2+7x+14\right)\)