Finite Math Examples

$(5 x - 2) (3 x - 4) - (5 x - 4) (4 x - 1)$

Step 1

Expand $(5 x - 2) (3 x - 4)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$5 x (3 x - 4) - 2 (3 x - 4) - (5 x - 4) (4 x - 1)$

Step 1.2

Apply the distributive property.

$5 x (3 x) + 5 x \cdot - 4 - 2 (3 x - 4) - (5 x - 4) (4 x - 1)$

Step 1.3

Apply the distributive property.

$5 x (3 x) + 5 x \cdot - 4 - 2 (3 x) - 2 \cdot - 4 - (5 x - 4) (4 x - 1)$

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Rewrite using the commutative property of multiplication.

$5 \cdot 3 x \cdot x + 5 x \cdot - 4 - 2 (3 x) - 2 \cdot - 4 - (5 x - 4) (4 x - 1)$

Step 2.1.2

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

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Step 2.1.2.1

Move $x$ .

$5 \cdot 3 (x \cdot x) + 5 x \cdot - 4 - 2 (3 x) - 2 \cdot - 4 - (5 x - 4) (4 x - 1)$

Step 2.1.2.2

Multiply $x$ by $x$ .

$5 \cdot 3 x^{2} + 5 x \cdot - 4 - 2 (3 x) - 2 \cdot - 4 - (5 x - 4) (4 x - 1)$

Step 2.1.3

Multiply $5$ by $3$ .

$15 x^{2} + 5 x \cdot - 4 - 2 (3 x) - 2 \cdot - 4 - (5 x - 4) (4 x - 1)$

Step 2.1.4

Multiply $- 4$ by $5$ .

$15 x^{2} - 20 x - 2 (3 x) - 2 \cdot - 4 - (5 x - 4) (4 x - 1)$

Step 2.1.5

Multiply $3$ by $- 2$ .

$15 x^{2} - 20 x - 6 x - 2 \cdot - 4 - (5 x - 4) (4 x - 1)$

Step 2.1.6

Multiply $- 2$ by $- 4$ .

$15 x^{2} - 20 x - 6 x + 8 - (5 x - 4) (4 x - 1)$

Step 2.2

Subtract $6 x$ from $- 20 x$ .

$15 x^{2} - 26 x + 8 - (5 x - 4) (4 x - 1)$

Step 3

Apply the distributive property.

$15 x^{2} - 26 x + 8 + (- (5 x) - - 4) (4 x - 1)$

Step 4

Multiply $5$ by $- 1$ .

$15 x^{2} - 26 x + 8 + (- 5 x - - 4) (4 x - 1)$

Step 5

Multiply $- 1$ by $- 4$ .

$15 x^{2} - 26 x + 8 + (- 5 x + 4) (4 x - 1)$

Step 6

Expand $(- 5 x + 4) (4 x - 1)$ using the FOIL Method.

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Step 6.1

Apply the distributive property.

$15 x^{2} - 26 x + 8 - 5 x (4 x - 1) + 4 (4 x - 1)$

Step 6.2

Apply the distributive property.

$15 x^{2} - 26 x + 8 - 5 x (4 x) - 5 x \cdot - 1 + 4 (4 x - 1)$

Step 6.3

Apply the distributive property.

$15 x^{2} - 26 x + 8 - 5 x (4 x) - 5 x \cdot - 1 + 4 (4 x) + 4 \cdot - 1$

Step 7

Simplify and combine like terms.

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Step 7.1

Simplify each term.

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Step 7.1.1

Rewrite using the commutative property of multiplication.

$15 x^{2} - 26 x + 8 - 5 \cdot 4 x \cdot x - 5 x \cdot - 1 + 4 (4 x) + 4 \cdot - 1$

Step 7.1.2

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

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Step 7.1.2.1

Move $x$ .

$15 x^{2} - 26 x + 8 - 5 \cdot 4 (x \cdot x) - 5 x \cdot - 1 + 4 (4 x) + 4 \cdot - 1$

Step 7.1.2.2

Multiply $x$ by $x$ .

$15 x^{2} - 26 x + 8 - 5 \cdot 4 x^{2} - 5 x \cdot - 1 + 4 (4 x) + 4 \cdot - 1$

Step 7.1.3

Multiply $- 5$ by $4$ .

$15 x^{2} - 26 x + 8 - 20 x^{2} - 5 x \cdot - 1 + 4 (4 x) + 4 \cdot - 1$

Step 7.1.4

Multiply $- 1$ by $- 5$ .

$15 x^{2} - 26 x + 8 - 20 x^{2} + 5 x + 4 (4 x) + 4 \cdot - 1$

Step 7.1.5

Multiply $4$ by $4$ .

$15 x^{2} - 26 x + 8 - 20 x^{2} + 5 x + 16 x + 4 \cdot - 1$

Step 7.1.6

Multiply $4$ by $- 1$ .

$15 x^{2} - 26 x + 8 - 20 x^{2} + 5 x + 16 x - 4$

Step 7.2

Add $5 x$ and $16 x$ .

$15 x^{2} - 26 x + 8 - 20 x^{2} + 21 x - 4$

Step 8

Subtract $20 x^{2}$ from $15 x^{2}$ .

$- 5 x^{2} - 26 x + 8 + 21 x - 4$

Step 9

Add $- 26 x$ and $21 x$ .

$- 5 x^{2} - 5 x + 8 - 4$

Step 10

Subtract $4$ from $8$ .

$- 5 x^{2} - 5 x + 4$

Step 11

Factor $- 1$ out of $- 5 x^{2} - 5 x + 4$ .

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Step 11.1

Factor $- 1$ out of $- 5 x^{2}$ .

$- (5 x^{2}) - 5 x + 4$

Step 11.2

Factor $- 1$ out of $- 5 x$ .

$- (5 x^{2}) - (5 x) + 4$

Step 11.3

Rewrite $4$ as $- 1 (- 4)$ .

$- (5 x^{2}) - (5 x) - 1 (- 4)$

Step 11.4

Factor $- 1$ out of $- (5 x^{2}) - (5 x)$ .

$- (5 x^{2} + 5 x) - 1 (- 4)$

Step 11.5

Factor $- 1$ out of $- (5 x^{2} + 5 x) - 1 (- 4)$ .

$- (5 x^{2} + 5 x - 4)$