Expand the Trigonometric Expression (4x+6)^3

${(4 x + 6)}^{3}$

Step 1

Use the Binomial Theorem.

${(4 x)}^{3} + 3 {(4 x)}^{2} \cdot 6 + 3 (4 x) \cdot 6^{2} + 6^{3}$

Step 2

Simplify each term.

Apply the product rule to $4 x$ .

$4^{3} x^{3} + 3 {(4 x)}^{2} \cdot 6 + 3 (4 x) \cdot 6^{2} + 6^{3}$

Raise $4$ to the power of $3$ .

$64 x^{3} + 3 {(4 x)}^{2} \cdot 6 + 3 (4 x) \cdot 6^{2} + 6^{3}$

Apply the product rule to $4 x$ .

$64 x^{3} + 3 (4^{2} x^{2}) \cdot 6 + 3 (4 x) \cdot 6^{2} + 6^{3}$

Raise $4$ to the power of $2$ .

$64 x^{3} + 3 (16 x^{2}) \cdot 6 + 3 (4 x) \cdot 6^{2} + 6^{3}$

Multiply $16$ by $3$ .

$64 x^{3} + 48 x^{2} \cdot 6 + 3 (4 x) \cdot 6^{2} + 6^{3}$

Multiply $6$ by $48$ .

$64 x^{3} + 288 x^{2} + 3 (4 x) \cdot 6^{2} + 6^{3}$

Multiply $4$ by $3$ .

$64 x^{3} + 288 x^{2} + 12 x \cdot 6^{2} + 6^{3}$

Raise $6$ to the power of $2$ .

$64 x^{3} + 288 x^{2} + 12 x \cdot 36 + 6^{3}$

Multiply $36$ by $12$ .

$64 x^{3} + 288 x^{2} + 432 x + 6^{3}$

Raise $6$ to the power of $3$ .

$64 x^{3} + 288 x^{2} + 432 x + 216$