Algebra Examples

$4 {(3 x - 2)}^{2} - 9 {(x - 1)}^{2}$

Step 1

Rewrite $4 {(3 x - 2)}^{2}$ as ${(2 (3 x - 2))}^{2}$ .

${(2 (3 x - 2))}^{2} - 9 {(x - 1)}^{2}$

Step 2

Rewrite $9 {(x - 1)}^{2}$ as ${(3 (x - 1))}^{2}$ .

${(2 (3 x - 2))}^{2} - {(3 (x - 1))}^{2}$

Step 3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 2 (3 x - 2)$ and $b = 3 (x - 1)$ .

$(2 (3 x - 2) + 3 (x - 1)) (2 (3 x - 2) - (3 (x - 1)))$

Step 4

Simplify.

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Step 4.1

Apply the distributive property.

$(2 (3 x) + 2 \cdot - 2 + 3 (x - 1)) (2 (3 x - 2) - (3 (x - 1)))$

Step 4.2

Multiply $3$ by $2$ .

$(6 x + 2 \cdot - 2 + 3 (x - 1)) (2 (3 x - 2) - (3 (x - 1)))$

Step 4.3

Multiply $2$ by $- 2$ .

$(6 x - 4 + 3 (x - 1)) (2 (3 x - 2) - (3 (x - 1)))$

Step 4.4

Apply the distributive property.

$(6 x - 4 + 3 x + 3 \cdot - 1) (2 (3 x - 2) - (3 (x - 1)))$

Step 4.5

Multiply $3$ by $- 1$ .

$(6 x - 4 + 3 x - 3) (2 (3 x - 2) - (3 (x - 1)))$

Step 4.6

Add $6 x$ and $3 x$ .

$(9 x - 4 - 3) (2 (3 x - 2) - (3 (x - 1)))$

Step 4.7

Subtract $3$ from $- 4$ .

$(9 x - 7) (2 (3 x - 2) - (3 (x - 1)))$

Step 4.8

Apply the distributive property.

$(9 x - 7) (2 (3 x) + 2 \cdot - 2 - (3 (x - 1)))$

Step 4.9

Multiply $3$ by $2$ .

$(9 x - 7) (6 x + 2 \cdot - 2 - (3 (x - 1)))$

Step 4.10

Multiply $2$ by $- 2$ .

$(9 x - 7) (6 x - 4 - (3 (x - 1)))$

Step 4.11

Apply the distributive property.

$(9 x - 7) (6 x - 4 - (3 x + 3 \cdot - 1))$

Step 4.12

Multiply $3$ by $- 1$ .

$(9 x - 7) (6 x - 4 - (3 x - 3))$

Step 4.13

Apply the distributive property.

$(9 x - 7) (6 x - 4 - (3 x) - - 3)$

Step 4.14

Multiply $3$ by $- 1$ .

$(9 x - 7) (6 x - 4 - 3 x - - 3)$

Step 4.15

Multiply $- 1$ by $- 3$ .

$(9 x - 7) (6 x - 4 - 3 x + 3)$

Step 4.16

Subtract $3 x$ from $6 x$ .

$(9 x - 7) (3 x - 4 + 3)$

Step 4.17

Add $- 4$ and $3$ .

$(9 x - 7) (3 x - 1)$