What is factor (x+5)^4+2(x+5)^2-1 ?

The solution to factor (x+5)^4+2(x+5)^2-1 is x^4+20x^3+152x^2+520x+674

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factor (x+5)^4+2(x+5)^2-1

factor

(x + 5)^{4} + 2 (x + 5)^{2} - 1

x^{4} + 20 x^{3} + 152 x^{2} + 520 x + 674

Solution steps

(x + 5)^{4} + 2 (x + 5)^{2} - 1

(x + 5)^{4} : x^{4} + 20 x^{3} + 150 x^{2} + 500 x + 625

= x^{4} + 20 x^{3} + 150 x^{2} + 500 x + 625 + 2 (x + 5)^{2} - 1

(x + 5)^{2} : x^{2} + 10 x + 25

= x^{4} + 20 x^{3} + 150 x^{2} + 500 x + 625 + 2 (x^{2} + 10 x + 25) - 1

Expand

2 (x^{2} + 10 x + 25) : 2 x^{2} + 20 x + 50

= x^{4} + 20 x^{3} + 150 x^{2} + 500 x + 625 + 2 x^{2} + 20 x + 50 - 1

Simplify

x^{4} + 20 x^{3} + 150 x^{2} + 500 x + 625 + 2 x^{2} + 20 x + 50 - 1 : x^{4} + 20 x^{3} + 152 x^{2} + 520 x + 674

= x^{4} + 20 x^{3} + 152 x^{2} + 520 x + 674

5 x^{3} - 7 x^{2}

[- 6.3]

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m^{3} - 216 n^{12} p^{3}

What is factor (x+5)^4+2(x+5)^2-1 ?
The solution to factor (x+5)^4+2(x+5)^2-1 is x^4+20x^3+152x^2+520x+674