Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

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

$(2 - x) (2 - x) + 3$

Step 1.2

Expand $(2 - x) (2 - x)$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

$2 (2 - x) - x (2 - x) + 3$

Step 1.2.2

Apply the distributive property.

$2 \cdot 2 + 2 (- x) - x (2 - x) + 3$

Step 1.2.3

Apply the distributive property.

$2 \cdot 2 + 2 (- x) - x \cdot 2 - x (- x) + 3$

$2 \cdot 2 + 2 (- x) - x \cdot 2 - x (- x) + 3$

Step 1.3

Simplify and combine like terms.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Multiply $2$ by $2$ .

$4 + 2 (- x) - x \cdot 2 - x (- x) + 3$

Step 1.3.1.2

Multiply $- 1$ by $2$ .

$4 - 2 x - x \cdot 2 - x (- x) + 3$

Step 1.3.1.3

Multiply $2$ by $- 1$ .

$4 - 2 x - 2 x - x (- x) + 3$

Step 1.3.1.4

Rewrite using the commutative property of multiplication.

$4 - 2 x - 2 x - 1 \cdot - 1 x \cdot x + 3$

Step 1.3.1.5

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

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Step 1.3.1.5.1

Move $x$ .

$4 - 2 x - 2 x - 1 \cdot - 1 (x \cdot x) + 3$

Step 1.3.1.5.2

Multiply $x$ by $x$ .

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

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

Step 1.3.1.6

Multiply $- 1$ by $- 1$ .

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

Step 1.3.1.7

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

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

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

Step 1.3.2

Subtract $2 x$ from $- 2 x$ .

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

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

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

Step 2

Add $4$ and $3$ .

$- 4 x + x^{2} + 7$

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