Simplify (2a-3b)^2

${(2 a - 3 b)}^{2}$

Step 1

Rewrite ${(2 a - 3 b)}^{2}$ as $(2 a - 3 b) (2 a - 3 b)$ .

$(2 a - 3 b) (2 a - 3 b)$

Step 2

Expand $(2 a - 3 b) (2 a - 3 b)$ using the FOIL Method.

Apply the distributive property.

$2 a (2 a - 3 b) - 3 b (2 a - 3 b)$

Apply the distributive property.

$2 a (2 a) + 2 a (- 3 b) - 3 b (2 a - 3 b)$

Apply the distributive property.

$2 a (2 a) + 2 a (- 3 b) - 3 b (2 a) - 3 b (- 3 b)$

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 \cdot 2 a \cdot a + 2 a (- 3 b) - 3 b (2 a) - 3 b (- 3 b)$

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

Move $a$ .

$2 \cdot 2 (a \cdot a) + 2 a (- 3 b) - 3 b (2 a) - 3 b (- 3 b)$

Multiply $a$ by $a$ .

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

Multiply $2$ by $2$ .

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

Rewrite using the commutative property of multiplication.

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

Multiply $2$ by $- 3$ .

$4 a^{2} - 6 a b - 3 b (2 a) - 3 b (- 3 b)$

Rewrite using the commutative property of multiplication.

$4 a^{2} - 6 a b - 3 \cdot 2 b a - 3 b (- 3 b)$

Multiply $- 3$ by $2$ .

$4 a^{2} - 6 a b - 6 b a - 3 b (- 3 b)$

Rewrite using the commutative property of multiplication.

$4 a^{2} - 6 a b - 6 b a - 3 \cdot - 3 b \cdot b$

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

Move $b$ .

$4 a^{2} - 6 a b - 6 b a - 3 \cdot - 3 (b \cdot b)$

Multiply $b$ by $b$ .

$4 a^{2} - 6 a b - 6 b a - 3 \cdot - 3 b^{2}$

Multiply $- 3$ by $- 3$ .

$4 a^{2} - 6 a b - 6 b a + 9 b^{2}$

Subtract $6 b a$ from $- 6 a b$ .

Move $b$ .

$4 a^{2} - 6 a b - 6 a b + 9 b^{2}$

Subtract $6 a b$ from $- 6 a b$ .

$4 a^{2} - 12 a b + 9 b^{2}$

Simplify (2a-3b)^2

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