Expand the Trigonometric Expression (6c+5d)(6c-5d)

$(6 c + 5 d) (6 c - 5 d)$

Step 1

Expand $(6 c + 5 d) (6 c - 5 d)$ using the FOIL Method.

Apply the distributive property.

$6 c (6 c - 5 d) + 5 d (6 c - 5 d)$

Apply the distributive property.

$6 c (6 c) + 6 c (- 5 d) + 5 d (6 c - 5 d)$

Apply the distributive property.

$6 c (6 c) + 6 c (- 5 d) + 5 d (6 c) + 5 d (- 5 d)$

Step 2

Simplify terms.

Combine the opposite terms in $6 c (6 c) + 6 c (- 5 d) + 5 d (6 c) + 5 d (- 5 d)$ .

Reorder the factors in the terms $6 c (- 5 d)$ and $5 d (6 c)$ .

$6 c (6 c) - 5 \cdot 6 c d + 5 \cdot 6 c d + 5 d (- 5 d)$

Add $- 5 \cdot 6 c d$ and $5 \cdot 6 c d$ .

$6 c (6 c) + 0 + 5 d (- 5 d)$

Add $6 c (6 c)$ and $0$ .

$6 c (6 c) + 5 d (- 5 d)$

Simplify each term.

Rewrite using the commutative property of multiplication.

$6 \cdot 6 c \cdot c + 5 d (- 5 d)$

Multiply $c$ by $c$ by adding the exponents.

Move $c$ .

$6 \cdot 6 (c \cdot c) + 5 d (- 5 d)$

Multiply $c$ by $c$ .

$6 \cdot 6 c^{2} + 5 d (- 5 d)$

Multiply $6$ by $6$ .

$36 c^{2} + 5 d (- 5 d)$

Rewrite using the commutative property of multiplication.

$36 c^{2} + 5 \cdot - 5 d \cdot d$

Multiply $d$ by $d$ by adding the exponents.

Move $d$ .

$36 c^{2} + 5 \cdot - 5 (d \cdot d)$

Multiply $d$ by $d$ .

$36 c^{2} + 5 \cdot - 5 d^{2}$

Multiply $5$ by $- 5$ .

$36 c^{2} - 25 d^{2}$