Expand the Trigonometric Expression (3k+4)(9k+5)

$(3 k + 4) (9 k + 5)$

Step 1

Expand $(3 k + 4) (9 k + 5)$ using the FOIL Method.

Apply the distributive property.

$3 k (9 k + 5) + 4 (9 k + 5)$

Apply the distributive property.

$3 k (9 k) + 3 k \cdot 5 + 4 (9 k + 5)$

Apply the distributive property.

$3 k (9 k) + 3 k \cdot 5 + 4 (9 k) + 4 \cdot 5$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$3 \cdot 9 k \cdot k + 3 k \cdot 5 + 4 (9 k) + 4 \cdot 5$

Multiply $k$ by $k$ by adding the exponents.

Move $k$ .

$3 \cdot 9 (k \cdot k) + 3 k \cdot 5 + 4 (9 k) + 4 \cdot 5$

Multiply $k$ by $k$ .

$3 \cdot 9 k^{2} + 3 k \cdot 5 + 4 (9 k) + 4 \cdot 5$

Multiply $3$ by $9$ .

$27 k^{2} + 3 k \cdot 5 + 4 (9 k) + 4 \cdot 5$

Multiply $5$ by $3$ .

$27 k^{2} + 15 k + 4 (9 k) + 4 \cdot 5$

Multiply $9$ by $4$ .

$27 k^{2} + 15 k + 36 k + 4 \cdot 5$

Multiply $4$ by $5$ .

$27 k^{2} + 15 k + 36 k + 20$

Add $15 k$ and $36 k$ .

$27 k^{2} + 51 k + 20$