Simplify (3b-4a)(3b-4a)

$(3 b - 4 a) (3 b - 4 a)$

Step 1

Expand $(3 b - 4 a) (3 b - 4 a)$ using the FOIL Method.

Apply the distributive property.

$3 b (3 b - 4 a) - 4 a (3 b - 4 a)$

Apply the distributive property.

$3 b (3 b) + 3 b (- 4 a) - 4 a (3 b - 4 a)$

Apply the distributive property.

$3 b (3 b) + 3 b (- 4 a) - 4 a (3 b) - 4 a (- 4 a)$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$3 \cdot 3 b \cdot b + 3 b (- 4 a) - 4 a (3 b) - 4 a (- 4 a)$

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

Move $b$ .

$3 \cdot 3 (b \cdot b) + 3 b (- 4 a) - 4 a (3 b) - 4 a (- 4 a)$

Multiply $b$ by $b$ .

$3 \cdot 3 b^{2} + 3 b (- 4 a) - 4 a (3 b) - 4 a (- 4 a)$

Multiply $3$ by $3$ .

$9 b^{2} + 3 b (- 4 a) - 4 a (3 b) - 4 a (- 4 a)$

Rewrite using the commutative property of multiplication.

$9 b^{2} + 3 \cdot - 4 b a - 4 a (3 b) - 4 a (- 4 a)$

Multiply $3$ by $- 4$ .

$9 b^{2} - 12 b a - 4 a (3 b) - 4 a (- 4 a)$

Rewrite using the commutative property of multiplication.

$9 b^{2} - 12 b a - 4 \cdot 3 a b - 4 a (- 4 a)$

Multiply $- 4$ by $3$ .

$9 b^{2} - 12 b a - 12 a b - 4 a (- 4 a)$

Rewrite using the commutative property of multiplication.

$9 b^{2} - 12 b a - 12 a b - 4 \cdot - 4 a \cdot a$

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

Move $a$ .

$9 b^{2} - 12 b a - 12 a b - 4 \cdot - 4 (a \cdot a)$

Multiply $a$ by $a$ .

$9 b^{2} - 12 b a - 12 a b - 4 \cdot - 4 a^{2}$

Multiply $- 4$ by $- 4$ .

$9 b^{2} - 12 b a - 12 a b + 16 a^{2}$

Subtract $12 a b$ from $- 12 b a$ .

Move $b$ .

$9 b^{2} - 12 a b - 12 a b + 16 a^{2}$

Subtract $12 a b$ from $- 12 a b$ .

$9 b^{2} - 24 a b + 16 a^{2}$

Step 3

Move $9 b^{2}$ .

$- 24 a b + 16 a^{2} + 9 b^{2}$

Step 4

Reorder $- 24 a b$ and $16 a^{2}$ .

$16 a^{2} - 24 a b + 9 b^{2}$

Simplify (3b-4a)(3b-4a)

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