Algebra Examples

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

Step 1

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

$x ((1 - x) (1 - x))$

Step 2

Expand $(1 - x) (1 - x)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$x (1 (1 - x) - x (1 - x))$

Step 2.2

Apply the distributive property.

$x (1 \cdot 1 + 1 (- x) - x (1 - x))$

Step 2.3

Apply the distributive property.

$x (1 \cdot 1 + 1 (- x) - x \cdot 1 - x (- x))$

$x (1 \cdot 1 + 1 (- x) - x \cdot 1 - x (- x))$

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $1$ by $1$ .

$x (1 + 1 (- x) - x \cdot 1 - x (- x))$

Step 3.1.2

Multiply $- x$ by $1$ .

$x (1 - x - x \cdot 1 - x (- x))$

Step 3.1.3

Multiply $- 1$ by $1$ .

$x (1 - x - x - x (- x))$

Step 3.1.4

Rewrite using the commutative property of multiplication.

$x (1 - x - x - 1 \cdot - 1 x \cdot x)$

Step 3.1.5

Multiply $x$ by $x$ by adding the exponents.

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Step 3.1.5.1

Move $x$ .

$x (1 - x - x - 1 \cdot - 1 (x \cdot x))$

Step 3.1.5.2

Multiply $x$ by $x$ .

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

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

Step 3.1.6

Multiply $- 1$ by $- 1$ .

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

Step 3.1.7

Multiply $x^{2}$ by $1$ .

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

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

Step 3.2

Subtract $x$ from $- x$ .

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

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

Step 4

Apply the distributive property.

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

Step 5

Simplify.

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Step 5.1

Multiply $x$ by $1$ .

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

Step 5.2

Rewrite using the commutative property of multiplication.

$x - 2 x \cdot x + x \cdot x^{2}$

Step 5.3

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

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Step 5.3.1

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

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Step 5.3.1.1

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

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

Step 5.3.1.2

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

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

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

Step 5.3.2

Add $1$ and $2$ .

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

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

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

Step 6

Multiply $x$ by $x$ by adding the exponents.

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Step 6.1

Move $x$ .

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

Step 6.2

Multiply $x$ by $x$ .

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

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

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$