Chemistry Examples

$(9 x - 1) (4 x - 2) - (6 x + 5) (9 x - 1)$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Expand $(9 x - 1) (4 x - 2)$ using the FOIL Method.

Tap for more steps...

Step 1.1.1

Apply the distributive property.

$9 x (4 x - 2) - 1 (4 x - 2) - (6 x + 5) (9 x - 1)$

Step 1.1.2

Apply the distributive property.

$9 x (4 x) + 9 x \cdot - 2 - 1 (4 x - 2) - (6 x + 5) (9 x - 1)$

Step 1.1.3

Apply the distributive property.

$9 x (4 x) + 9 x \cdot - 2 - 1 (4 x) - 1 \cdot - 2 - (6 x + 5) (9 x - 1)$

Step 1.2

Simplify and combine like terms.

Tap for more steps...

Step 1.2.1

Simplify each term.

Tap for more steps...

Step 1.2.1.1

Rewrite using the commutative property of multiplication.

$9 \cdot 4 x \cdot x + 9 x \cdot - 2 - 1 (4 x) - 1 \cdot - 2 - (6 x + 5) (9 x - 1)$

Step 1.2.1.2

Multiply $x$ by $x$ by adding the exponents.

Tap for more steps...

Step 1.2.1.2.1

Move $x$ .

$9 \cdot 4 (x \cdot x) + 9 x \cdot - 2 - 1 (4 x) - 1 \cdot - 2 - (6 x + 5) (9 x - 1)$

Step 1.2.1.2.2

Multiply $x$ by $x$ .

$9 \cdot 4 x^{2} + 9 x \cdot - 2 - 1 (4 x) - 1 \cdot - 2 - (6 x + 5) (9 x - 1)$

Step 1.2.1.3

Multiply $9$ by $4$ .

$36 x^{2} + 9 x \cdot - 2 - 1 (4 x) - 1 \cdot - 2 - (6 x + 5) (9 x - 1)$

Step 1.2.1.4

Multiply $- 2$ by $9$ .

$36 x^{2} - 18 x - 1 (4 x) - 1 \cdot - 2 - (6 x + 5) (9 x - 1)$

Step 1.2.1.5

Multiply $4$ by $- 1$ .

$36 x^{2} - 18 x - 4 x - 1 \cdot - 2 - (6 x + 5) (9 x - 1)$

Step 1.2.1.6

Multiply $- 1$ by $- 2$ .

$36 x^{2} - 18 x - 4 x + 2 - (6 x + 5) (9 x - 1)$

Step 1.2.2

Subtract $4 x$ from $- 18 x$ .

$36 x^{2} - 22 x + 2 - (6 x + 5) (9 x - 1)$

Step 1.3

Apply the distributive property.

$36 x^{2} - 22 x + 2 + (- (6 x) - 1 \cdot 5) (9 x - 1)$

Step 1.4

Multiply $6$ by $- 1$ .

$36 x^{2} - 22 x + 2 + (- 6 x - 1 \cdot 5) (9 x - 1)$

Step 1.5

Multiply $- 1$ by $5$ .

$36 x^{2} - 22 x + 2 + (- 6 x - 5) (9 x - 1)$

Step 1.6

Expand $(- 6 x - 5) (9 x - 1)$ using the FOIL Method.

Tap for more steps...

Step 1.6.1

Apply the distributive property.

$36 x^{2} - 22 x + 2 - 6 x (9 x - 1) - 5 (9 x - 1)$

Step 1.6.2

Apply the distributive property.

$36 x^{2} - 22 x + 2 - 6 x (9 x) - 6 x \cdot - 1 - 5 (9 x - 1)$

Step 1.6.3

Apply the distributive property.

$36 x^{2} - 22 x + 2 - 6 x (9 x) - 6 x \cdot - 1 - 5 (9 x) - 5 \cdot - 1$

Step 1.7

Simplify and combine like terms.

Tap for more steps...

Step 1.7.1

Simplify each term.

Tap for more steps...

Step 1.7.1.1

Rewrite using the commutative property of multiplication.

$36 x^{2} - 22 x + 2 - 6 \cdot 9 x \cdot x - 6 x \cdot - 1 - 5 (9 x) - 5 \cdot - 1$

Step 1.7.1.2

Multiply $x$ by $x$ by adding the exponents.

Tap for more steps...

Step 1.7.1.2.1

Move $x$ .

$36 x^{2} - 22 x + 2 - 6 \cdot 9 (x \cdot x) - 6 x \cdot - 1 - 5 (9 x) - 5 \cdot - 1$

Step 1.7.1.2.2

Multiply $x$ by $x$ .

$36 x^{2} - 22 x + 2 - 6 \cdot 9 x^{2} - 6 x \cdot - 1 - 5 (9 x) - 5 \cdot - 1$

Step 1.7.1.3

Multiply $- 6$ by $9$ .

$36 x^{2} - 22 x + 2 - 54 x^{2} - 6 x \cdot - 1 - 5 (9 x) - 5 \cdot - 1$

Step 1.7.1.4

Multiply $- 1$ by $- 6$ .

$36 x^{2} - 22 x + 2 - 54 x^{2} + 6 x - 5 (9 x) - 5 \cdot - 1$

Step 1.7.1.5

Multiply $9$ by $- 5$ .

$36 x^{2} - 22 x + 2 - 54 x^{2} + 6 x - 45 x - 5 \cdot - 1$

Step 1.7.1.6

Multiply $- 5$ by $- 1$ .

$36 x^{2} - 22 x + 2 - 54 x^{2} + 6 x - 45 x + 5$

Step 1.7.2

Subtract $45 x$ from $6 x$ .

$36 x^{2} - 22 x + 2 - 54 x^{2} - 39 x + 5$

Step 2

Simplify by adding terms.

Tap for more steps...

Step 2.1

Subtract $54 x^{2}$ from $36 x^{2}$ .

$- 18 x^{2} - 22 x + 2 - 39 x + 5$

Step 2.2

Subtract $39 x$ from $- 22 x$ .

$- 18 x^{2} - 61 x + 2 + 5$

Step 2.3

Add $2$ and $5$ .

$- 18 x^{2} - 61 x + 7$