Simplify (-4x)/11(121x+22)

$\frac{- 4 x}{11} (121 x + 22)$

Step 1

Move the negative in front of the fraction.

$- \frac{(4) x}{11} \cdot (121 x + 22)$

Step 2

Apply the distributive property.

$- \frac{4 x}{11} (121 x) - \frac{4 x}{11} \cdot 22$

Step 3

Cancel the common factor of $11$ .

Move the leading negative in $- \frac{4 x}{11}$ into the numerator.

$\frac{- 4 x}{11} (121 x) - \frac{4 x}{11} \cdot 22$

Factor $11$ out of $121 x$ .

$\frac{- 4 x}{11} (11 (11 x)) - \frac{4 x}{11} \cdot 22$

Cancel the common factor.

$\frac{- 4 x}{11} (11 (11 x)) - \frac{4 x}{11} \cdot 22$

Rewrite the expression.

$- 4 x (11 x) - \frac{4 x}{11} \cdot 22$

Step 4

Multiply $11$ by $- 4$ .

$- 44 x \cdot x - \frac{4 x}{11} \cdot 22$

Step 5

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

$- 44 (x^{1} x) - \frac{4 x}{11} \cdot 22$

Step 6

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

$- 44 (x^{1} x^{1}) - \frac{4 x}{11} \cdot 22$

Step 7

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

$- 44 x^{1 + 1} - \frac{4 x}{11} \cdot 22$

Step 8

Add $1$ and $1$ .

$- 44 x^{2} - \frac{4 x}{11} \cdot 22$

Step 9

Cancel the common factor of $11$ .

Move the leading negative in $- \frac{4 x}{11}$ into the numerator.

$- 44 x^{2} + \frac{- 4 x}{11} \cdot 22$

Factor $11$ out of $22$ .

$- 44 x^{2} + \frac{- 4 x}{11} \cdot (11 (2))$

Cancel the common factor.

$- 44 x^{2} + \frac{- 4 x}{11} \cdot (11 \cdot 2)$

Rewrite the expression.

$- 44 x^{2} - 4 x \cdot 2$

Step 10

Multiply $2$ by $- 4$ .

$- 44 x^{2} - 8 x$