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

The solution to expand (x-1)^3(x+1)^2 is x^5-x^4-2x^3+2x^2+x-1

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

expand

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

x^{5} - x^{4} - 2 x^{3} + 2 x^{2} + x - 1

Solution steps

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

Expand

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

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

Expand

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

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

Distribute parentheses

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

Simplify

x^{3} x^{2} + x^{3} \cdot 2 x + x^{3} \cdot 1 - 3 x^{2} x^{2} - 3 x^{2} \cdot 2 x - 3 x^{2} \cdot 1 + 3 x x^{2} + 3 x \cdot 2 x + 3 x \cdot 1 - 1 \cdot x^{2} - 1 \cdot 2 x - 1 \cdot 1 : x^{5} - x^{4} - 2 x^{3} + 2 x^{2} + x - 1

= x^{5} - x^{4} - 2 x^{3} + 2 x^{2} + x - 1

\frac{( a + b )}{( \frac{a}{12} + \frac{b}{6} )}

(\frac{4}{5 \cdot p - 3 q})^{2}

(x^{3} y^{3})^{2} + (2 x^{2} y^{2})^{3}

\frac{- 5}{( 3 - 2 x )}

\frac{( 2 x ^{2} - 9 x - 56 )}{( x - 8 )}

What is expand (x-1)^3(x+1)^2 ?
The solution to expand (x-1)^3(x+1)^2 is x^5-x^4-2x^3+2x^2+x-1