Simplify x^2(x-1)^3

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

Step 1

Use the Binomial Theorem.

$x^{2} (x^{3} + 3 x^{2} \cdot - 1 + 3 x {(- 1)}^{2} + {(- 1)}^{3})$

Step 2

Simplify terms.

Simplify each term.

Multiply $- 1$ by $3$ .

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

Raise $- 1$ to the power of $2$ .

$x^{2} (x^{3} - 3 x^{2} + 3 x \cdot 1 + {(- 1)}^{3})$

Multiply $3$ by $1$ .

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

Raise $- 1$ to the power of $3$ .

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

Apply the distributive property.

$x^{2} x^{3} + x^{2} (- 3 x^{2}) + x^{2} (3 x) + x^{2} \cdot - 1$

Step 3

Simplify.

Multiply $x^{2}$ by $x^{3}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{2 + 3} + x^{2} (- 3 x^{2}) + x^{2} (3 x) + x^{2} \cdot - 1$

Add $2$ and $3$ .

$x^{5} + x^{2} (- 3 x^{2}) + x^{2} (3 x) + x^{2} \cdot - 1$

Rewrite using the commutative property of multiplication.

$x^{5} - 3 x^{2} x^{2} + x^{2} (3 x) + x^{2} \cdot - 1$

Rewrite using the commutative property of multiplication.

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

Move $- 1$ to the left of $x^{2}$ .

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

Step 4

Simplify each term.

Multiply $x^{2}$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

$x^{5} - 3 (x^{2} x^{2}) + 3 x^{2} x - 1 \cdot x^{2}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add $2$ and $2$ .

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

Multiply $x^{2}$ by $x$ by adding the exponents.

Move $x$ .

$x^{5} - 3 x^{4} + 3 (x \cdot x^{2}) - 1 \cdot x^{2}$

Multiply $x$ by $x^{2}$ .

Raise $x$ to the power of $1$ .

$x^{5} - 3 x^{4} + 3 (x^{1} x^{2}) - 1 \cdot x^{2}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add $1$ and $2$ .

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

Rewrite $- 1 x^{2}$ as $- x^{2}$ .

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

Simplify x^2(x-1)^3

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