Expand the Trigonometric Expression (24x^2+28xk+4k^2)/(6x+6k)

$\frac{24 x^{2} + 28 x k + 4 k^{2}}{6 x + 6 k}$

Step 1

Cancel the common factor of $24 x^{2} + 28 x k + 4 k^{2}$ and $6 x + 6 k$ .

Factor $2$ out of $24 x^{2}$ .

$\frac{2 (12 x^{2}) + 28 x k + 4 k^{2}}{6 x + 6 k}$

Factor $2$ out of $28 x k$ .

$\frac{2 (12 x^{2}) + 2 (14 x k) + 4 k^{2}}{6 x + 6 k}$

Factor $2$ out of $2 (12 x^{2}) + 2 (14 x k)$ .

$\frac{2 (12 x^{2} + 14 x k) + 4 k^{2}}{6 x + 6 k}$

Factor $2$ out of $4 k^{2}$ .

$\frac{2 (12 x^{2} + 14 x k) + 2 (2 k^{2})}{6 x + 6 k}$

Factor $2$ out of $2 (12 x^{2} + 14 x k) + 2 (2 k^{2})$ .

$\frac{2 (12 x^{2} + 14 x k + 2 k^{2})}{6 x + 6 k}$

Cancel the common factors.

Factor $2$ out of $6 x$ .

$\frac{2 (12 x^{2} + 14 x k + 2 k^{2})}{2 (3 x) + 6 k}$

Factor $2$ out of $6 k$ .

$\frac{2 (12 x^{2} + 14 x k + 2 k^{2})}{2 (3 x) + 2 (3 k)}$

Factor $2$ out of $2 (3 x) + 2 (3 k)$ .

$\frac{2 (12 x^{2} + 14 x k + 2 k^{2})}{2 (3 x + 3 k)}$

Cancel the common factor.

$\frac{2 (12 x^{2} + 14 x k + 2 k^{2})}{2 (3 x + 3 k)}$

Rewrite the expression.

$\frac{12 x^{2} + 14 x k + 2 k^{2}}{3 x + 3 k}$

Step 2

Simplify the numerator.

Factor $2$ out of $12 x^{2} + 14 x k + 2 k^{2}$ .

Factor $2$ out of $12 x^{2}$ .

$\frac{2 (6 x^{2}) + 14 x k + 2 k^{2}}{3 x + 3 k}$

Factor $2$ out of $14 x k$ .

$\frac{2 (6 x^{2}) + 2 (7 x k) + 2 k^{2}}{3 x + 3 k}$

Factor $2$ out of $2 k^{2}$ .

$\frac{2 (6 x^{2}) + 2 (7 x k) + 2 (k^{2})}{3 x + 3 k}$

Factor $2$ out of $2 (6 x^{2}) + 2 (7 x k)$ .

$\frac{2 (6 x^{2} + 7 x k) + 2 (k^{2})}{3 x + 3 k}$

Factor $2$ out of $2 (6 x^{2} + 7 x k) + 2 (k^{2})$ .

$\frac{2 (6 x^{2} + 7 x k + k^{2})}{3 x + 3 k}$

Factor by grouping.

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 1 \cdot 6 = 6$ and whose sum is $b = 7$ .

Reorder terms.

$\frac{2 (k^{2} + 6 x^{2} + 7 k x)}{3 x + 3 k}$

Reorder $6 x^{2}$ and $7 k x$ .

$\frac{2 (k^{2} + 7 k x + 6 x^{2})}{3 x + 3 k}$

Factor $7$ out of $7 k x$ .

$\frac{2 (k^{2} + 7 (k x) + 6 x^{2})}{3 x + 3 k}$

Rewrite $7$ as $1$ plus $6$

$\frac{2 (k^{2} + (1 + 6) (k x) + 6 x^{2})}{3 x + 3 k}$

Apply the distributive property.

$\frac{2 (k^{2} + 1 (k x) + 6 (k x) + 6 x^{2})}{3 x + 3 k}$

Multiply $k x$ by $1$ .

$\frac{2 (k^{2} + k x + 6 (k x) + 6 x^{2})}{3 x + 3 k}$

Move parentheses.

$\frac{2 (k^{2} + k x + 6 k x + 6 x^{2})}{3 x + 3 k}$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$\frac{2 ((k^{2} + k x) + 6 k x + 6 x^{2})}{3 x + 3 k}$

Factor out the greatest common factor (GCF) from each group.

$\frac{2 (k (k + x) + 6 x (k + x))}{3 x + 3 k}$

Factor the polynomial by factoring out the greatest common factor, $k + x$ .

$\frac{2 ((k + x) (k + 6 x))}{3 x + 3 k}$

$\frac{2 (k + x) (k + 6 x)}{3 x + 3 k}$

Step 3

Simplify terms.

Factor $3$ out of $3 x + 3 k$ .

Factor $3$ out of $3 x$ .

$\frac{2 (k + x) (k + 6 x)}{3 (x) + 3 k}$

Factor $3$ out of $3 k$ .

$\frac{2 (k + x) (k + 6 x)}{3 (x) + 3 (k)}$

Factor $3$ out of $3 (x) + 3 (k)$ .

$\frac{2 (k + x) (k + 6 x)}{3 (x + k)}$

Cancel the common factor of $k + x$ and $x + k$ .

Reorder terms.

$\frac{2 (k + x) (k + 6 x)}{3 (k + x)}$

Cancel the common factor.

$\frac{2 (k + x) (k + 6 x)}{3 (k + x)}$

Rewrite the expression.

$\frac{2 (k + 6 x)}{3}$

Expand the Trigonometric Expression (24x^2+28xk+4k^2)/(6x+6k)

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