Simplify (6ab+5c)(6ab-5c)

$(6 a b + 5 c) (6 a b - 5 c)$

Step 1

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

Apply the distributive property.

$6 a b (6 a b - 5 c) + 5 c (6 a b - 5 c)$

Apply the distributive property.

$6 a b (6 a b) + 6 a b (- 5 c) + 5 c (6 a b - 5 c)$

Apply the distributive property.

$6 a b (6 a b) + 6 a b (- 5 c) + 5 c (6 a b) + 5 c (- 5 c)$

Step 2

Simplify terms.

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

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

$6 a b (6 a b) - 5 \cdot 6 a b c + 5 \cdot 6 a b c + 5 c (- 5 c)$

Add $- 5 \cdot 6 a b c$ and $5 \cdot 6 a b c$ .

$6 a b (6 a b) + 0 + 5 c (- 5 c)$

Add $6 a b (6 a b)$ and $0$ .

$6 a b (6 a b) + 5 c (- 5 c)$

Simplify each term.

Multiply $a$ by $a$ by adding the exponents.

Move $a$ .

$6 (a \cdot a) b (6 b) + 5 c (- 5 c)$

Multiply $a$ by $a$ .

$6 a^{2} b (6 b) + 5 c (- 5 c)$

Multiply $b$ by $b$ by adding the exponents.

Move $b$ .

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

Multiply $b$ by $b$ .

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

Multiply $6$ by $6$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $c$ .

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

Multiply $c$ by $c$ .

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

Multiply $5$ by $- 5$ .

$36 a^{2} b^{2} - 25 c^{2}$