Expand the Trigonometric Expression (4/5kj-6)^2

${(\frac{4}{5} k j - 6)}^{2}$

Step 1

Simplify terms.

Simplify each term.

Combine $\frac{4}{5}$ and $k$ .

${(\frac{4 k}{5} j - 6)}^{2}$

Combine $\frac{4 k}{5}$ and $j$ .

${(\frac{4 k j}{5} - 6)}^{2}$

Rewrite ${(\frac{4 k j}{5} - 6)}^{2}$ as $(\frac{4 k j}{5} - 6) (\frac{4 k j}{5} - 6)$ .

$(\frac{4 k j}{5} - 6) (\frac{4 k j}{5} - 6)$

Step 2

Expand $(\frac{4 k j}{5} - 6) (\frac{4 k j}{5} - 6)$ using the FOIL Method.

Apply the distributive property.

$\frac{4 k j}{5} (\frac{4 k j}{5} - 6) - 6 (\frac{4 k j}{5} - 6)$

Apply the distributive property.

$\frac{4 k j}{5} \cdot \frac{4 k j}{5} + \frac{4 k j}{5} \cdot - 6 - 6 (\frac{4 k j}{5} - 6)$

Apply the distributive property.

$\frac{4 k j}{5} \cdot \frac{4 k j}{5} + \frac{4 k j}{5} \cdot - 6 - 6 \frac{4 k j}{5} - 6 \cdot - 6$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $\frac{4 k j}{5} \cdot \frac{4 k j}{5}$ .

Multiply $\frac{4 k j}{5}$ by $\frac{4 k j}{5}$ .

$\frac{4 k j (4 k j)}{5 \cdot 5} + \frac{4 k j}{5} \cdot - 6 - 6 \frac{4 k j}{5} - 6 \cdot - 6$

Multiply $4$ by $4$ .

$\frac{16 k j (k j)}{5 \cdot 5} + \frac{4 k j}{5} \cdot - 6 - 6 \frac{4 k j}{5} - 6 \cdot - 6$

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

$\frac{16 j (k^{1} k j)}{5 \cdot 5} + \frac{4 k j}{5} \cdot - 6 - 6 \frac{4 k j}{5} - 6 \cdot - 6$

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

$\frac{16 j (k^{1} k^{1} j)}{5 \cdot 5} + \frac{4 k j}{5} \cdot - 6 - 6 \frac{4 k j}{5} - 6 \cdot - 6$

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

$\frac{16 j (k^{1 + 1} j)}{5 \cdot 5} + \frac{4 k j}{5} \cdot - 6 - 6 \frac{4 k j}{5} - 6 \cdot - 6$

Add $1$ and $1$ .

$\frac{16 j (k^{2} j)}{5 \cdot 5} + \frac{4 k j}{5} \cdot - 6 - 6 \frac{4 k j}{5} - 6 \cdot - 6$

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

$\frac{16 (j^{1} j) k^{2}}{5 \cdot 5} + \frac{4 k j}{5} \cdot - 6 - 6 \frac{4 k j}{5} - 6 \cdot - 6$

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

$\frac{16 (j^{1} j^{1}) k^{2}}{5 \cdot 5} + \frac{4 k j}{5} \cdot - 6 - 6 \frac{4 k j}{5} - 6 \cdot - 6$

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

$\frac{16 j^{1 + 1} k^{2}}{5 \cdot 5} + \frac{4 k j}{5} \cdot - 6 - 6 \frac{4 k j}{5} - 6 \cdot - 6$

Add $1$ and $1$ .

$\frac{16 j^{2} k^{2}}{5 \cdot 5} + \frac{4 k j}{5} \cdot - 6 - 6 \frac{4 k j}{5} - 6 \cdot - 6$

Multiply $5$ by $5$ .

$\frac{16 j^{2} k^{2}}{25} + \frac{4 k j}{5} \cdot - 6 - 6 \frac{4 k j}{5} - 6 \cdot - 6$

Multiply $\frac{4 k j}{5} \cdot - 6$ .

Combine $\frac{4 k j}{5}$ and $- 6$ .

$\frac{16 j^{2} k^{2}}{25} + \frac{4 k j \cdot - 6}{5} - 6 \frac{4 k j}{5} - 6 \cdot - 6$

Multiply $- 6$ by $4$ .

$\frac{16 j^{2} k^{2}}{25} + \frac{- 24 k j}{5} - 6 \frac{4 k j}{5} - 6 \cdot - 6$

Move the negative in front of the fraction.

$\frac{16 j^{2} k^{2}}{25} - \frac{(24) k j}{5} - 6 \frac{4 k j}{5} - 6 \cdot - 6$

Multiply $- 6 \frac{4 k j}{5}$ .

Combine $- 6$ and $\frac{4 k j}{5}$ .

$\frac{16 j^{2} k^{2}}{25} - \frac{24 k j}{5} + \frac{- 6 (4 k j)}{5} - 6 \cdot - 6$

Multiply $4$ by $- 6$ .

$\frac{16 j^{2} k^{2}}{25} - \frac{24 k j}{5} + \frac{- 24 (k j)}{5} - 6 \cdot - 6$

Move the negative in front of the fraction.

$\frac{16 j^{2} k^{2}}{25} - \frac{24 k j}{5} - \frac{(24) k j}{5} - 6 \cdot - 6$

Multiply $- 6$ by $- 6$ .

$\frac{16 j^{2} k^{2}}{25} - \frac{24 k j}{5} - \frac{24 k j}{5} + 36$

Subtract $\frac{24 k j}{5}$ from $- \frac{24 k j}{5}$ .

$\frac{16 j^{2} k^{2}}{25} - 2 \frac{24 k j}{5} + 36$

Step 4

Simplify each term.

Multiply $- 2 \frac{24 k j}{5}$ .

Combine $- 2$ and $\frac{24 k j}{5}$ .

$\frac{16 j^{2} k^{2}}{25} + \frac{- 2 (24 k j)}{5} + 36$

Multiply $24$ by $- 2$ .

$\frac{16 j^{2} k^{2}}{25} + \frac{- 48 (k j)}{5} + 36$

Move the negative in front of the fraction.

$\frac{16 j^{2} k^{2}}{25} - \frac{48 k j}{5} + 36$

Expand the Trigonometric Expression (4/5kj-6)^2

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