Factor
$$(x+1)^4+(x+3)^4-272$$

Question

Uniteasy Admin · Accepted Answer

Given $$(x+1)^4+(x+3)^4-272$$
Let
$$y = x+2$$n
then
$$(x+1)^4+(x+3)^4-272$$
$$=(y-1)^4+(y+1)^4-272$$
$$=(y^2-2y+1)^2+(y^2+2y+1)^2-272$$
$$=(y^2+1)^2-4y(y^2+1)+4y^2+(y^2+1)^2+4y(y^2+1)+4y^2-272$$
$$=2(y^2+1)^2+8y^2-272$$
$$=2y^4+12y^2-270$$
$$=2(y^4+6y^2-135)$$
$$=2(y^2-9)(y^2+15)$$
$$ =2(y-3)(y+3)(y^2+15) $$
Substitute (1) then
$$(x+1)^4+(x+3)^4-272 = 2(x+5)(x-1)(x^2+4x+19)$$

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