Pre-Algebra Examples

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

Step 1

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

$(2 b - 3 c) (2 b - 3 c)$

Step 2

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

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Step 2.1

Apply the distributive property.

$2 b (2 b - 3 c) - 3 c (2 b - 3 c)$

Step 2.2

Apply the distributive property.

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

Step 2.3

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Rewrite using the commutative property of multiplication.

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

Step 3.1.2

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

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Step 3.1.2.1

Move $b$ .

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

Step 3.1.2.2

Multiply $b$ by $b$ .

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

Step 3.1.3

Multiply $2$ by $2$ .

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

Step 3.1.4

Rewrite using the commutative property of multiplication.

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

Step 3.1.5

Multiply $2$ by $- 3$ .

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

Step 3.1.6

Rewrite using the commutative property of multiplication.

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

Step 3.1.7

Multiply $- 3$ by $2$ .

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

Step 3.1.8

Rewrite using the commutative property of multiplication.

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

Step 3.1.9

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

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Step 3.1.9.1

Move $c$ .

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

Step 3.1.9.2

Multiply $c$ by $c$ .

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

Step 3.1.10

Multiply $- 3$ by $- 3$ .

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

Step 3.2

Subtract $6 c b$ from $- 6 b c$ .

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Step 3.2.1

Move $c$ .

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

Step 3.2.2

Subtract $6 b c$ from $- 6 b c$ .

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