What is (x-1)^2+(x-1)^3 ?

The solution to (x-1)^2+(x-1)^3 is x^3-2x^2+x

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simplify (x-1)^2+(x-1)^3

simplify

(x - 1)^{2} + (x - 1)^{3}

x^{3} - 2 x^{2} + x

Solution steps

(x - 1)^{2} + (x - 1)^{3}

Expand

(x - 1)^{2} : x^{2} - 2 x + 1

= x^{2} - 2 x + 1 + (x - 1)^{3}

Expand

(x - 1)^{3} : x^{3} - 3 x^{2} + 3 x - 1

= x^{2} - 2 x + 1 + x^{3} - 3 x^{2} + 3 x - 1

Group like terms

= x^{3} + x^{2} - 3 x^{2} - 2 x + 3 x + 1 - 1

Add similar elements:

x^{2} - 3 x^{2} = - 2 x^{2}

= x^{3} - 2 x^{2} - 2 x + 3 x + 1 - 1

Add similar elements:

- 2 x + 3 x = x

= x^{3} - 2 x^{2} + x + 1 - 1

Subtract the numbers:

1 - 1 = 0

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

\frac{( 8 x ^{3} - 1 )}{( 2 x - 1 )}

\frac{( 4 + h - 2 )}{h}

\frac{6 ^{- 5}}{1 0 ^{- 3}}

4384

\frac{8}{5} - \frac{6}{4}