What is (x-5)^3+(5+x^3) ?

The solution to (x-5)^3+(5+x^3) is 2x^3-15x^2+75x-120

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simplify (x-5)^3+(5+x^3)

simplify

(x - 5)^{3} + (5 + x^{3})

2 x^{3} - 15 x^{2} + 75 x - 120

Solution steps

(x - 5)^{3} + (5 + x^{3})

Apply rule:

a + (b + c) = a + b + c

(x - 5)^{3} + (5 + x^{3}) = (x - 5)^{3} + 5 + x^{3}

= (x - 5)^{3} + 5 + x^{3}

Expand

(x - 5)^{3} : x^{3} - 15 x^{2} + 75 x - 125

= x^{3} - 15 x^{2} + 75 x - 125 + 5 + x^{3}

Group like terms

= x^{3} + x^{3} - 15 x^{2} + 75 x - 125 + 5

Add similar elements:

x^{3} + x^{3} = 2 x^{3}

= 2 x^{3} - 15 x^{2} + 75 x - 125 + 5

Add the numbers:

- 125 + 5 = - 120

= 2 x^{3} - 15 x^{2} + 75 x - 120

p_{1} (x) + p_{2} (x)

\frac{cos ( 9 x )}{sin ( x )}

p^{2} + 20.2 p^{2} + 6 p + 7.5 p^{2} - 4 p + 15

ln (1) + x

1 - 50 x^{2} + 625 x^{4}