Precalculus Examples

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

Step 1

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

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

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

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $1$ by $1$ .

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

Step 2.1.2

Multiply $- x$ by $1$ .

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

Step 2.1.3

Multiply $- 1$ by $1$ .

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

Step 2.1.4

Rewrite using the commutative property of multiplication.

$1 - x - x - 1 \cdot - 1 x \cdot x$

Step 2.1.5

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

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Step 2.1.5.1

Move $x$ .

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

Step 2.1.5.2

Multiply $x$ by $x$ .

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

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

Step 2.1.6

Multiply $- 1$ by $- 1$ .

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

Step 2.1.7

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

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

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

Step 2.2

Subtract $x$ from $- x$ .

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

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

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