Find the Domain v=x(11-2x)(11-2x)

$v = x (11 - 2 x) (11 - 2 x)$

Step 1

Simplify $x (11 - 2 x) (11 - 2 x)$ .

Simplify terms.

Apply the distributive property.

$v = (x \cdot 11 + x (- 2 x)) (11 - 2 x)$

Reorder.

Move $11$ to the left of $x$ .

$v = (11 \cdot x + x (- 2 x)) (11 - 2 x)$

Rewrite using the commutative property of multiplication.

$v = (11 \cdot x - 2 x \cdot x) (11 - 2 x)$

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

Move $x$ .

$v = (11 x - 2 (x \cdot x)) (11 - 2 x)$

Multiply $x$ by $x$ .

$v = (11 x - 2 x^{2}) (11 - 2 x)$

Expand $(11 x - 2 x^{2}) (11 - 2 x)$ using the FOIL Method.

Apply the distributive property.

$v = 11 x (11 - 2 x) - 2 x^{2} (11 - 2 x)$

Apply the distributive property.

$v = 11 x \cdot 11 + 11 x (- 2 x) - 2 x^{2} (11 - 2 x)$

Apply the distributive property.

$v = 11 x \cdot 11 + 11 x (- 2 x) - 2 x^{2} \cdot 11 - 2 x^{2} (- 2 x)$

Simplify and combine like terms.

Simplify each term.

Multiply $11$ by $11$ .

$v = 121 x + 11 x (- 2 x) - 2 x^{2} \cdot 11 - 2 x^{2} (- 2 x)$

Rewrite using the commutative property of multiplication.

$v = 121 x + 11 \cdot - 2 x \cdot x - 2 x^{2} \cdot 11 - 2 x^{2} (- 2 x)$

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

Move $x$ .

$v = 121 x + 11 \cdot - 2 (x \cdot x) - 2 x^{2} \cdot 11 - 2 x^{2} (- 2 x)$

Multiply $x$ by $x$ .

$v = 121 x + 11 \cdot - 2 x^{2} - 2 x^{2} \cdot 11 - 2 x^{2} (- 2 x)$

Multiply $11$ by $- 2$ .

$v = 121 x - 22 x^{2} - 2 x^{2} \cdot 11 - 2 x^{2} (- 2 x)$

Multiply $11$ by $- 2$ .

$v = 121 x - 22 x^{2} - 22 x^{2} - 2 x^{2} (- 2 x)$

Rewrite using the commutative property of multiplication.

$v = 121 x - 22 x^{2} - 22 x^{2} - 2 \cdot - 2 x^{2} x$

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

Move $x$ .

$v = 121 x - 22 x^{2} - 22 x^{2} - 2 \cdot - 2 (x \cdot x^{2})$

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

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

$v = 121 x - 22 x^{2} - 22 x^{2} - 2 \cdot - 2 (x^{1} x^{2})$

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

$v = 121 x - 22 x^{2} - 22 x^{2} - 2 \cdot - 2 x^{1 + 2}$

Add $1$ and $2$ .

$v = 121 x - 22 x^{2} - 22 x^{2} - 2 \cdot - 2 x^{3}$

Multiply $- 2$ by $- 2$ .

$v = 121 x - 22 x^{2} - 22 x^{2} + 4 x^{3}$

Subtract $22 x^{2}$ from $- 22 x^{2}$ .

$v = 121 x - 44 x^{2} + 4 x^{3}$

Step 2

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$

Step 3

Find the Domain v=x(11-2x)(11-2x)

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