Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Apply the distributive property.

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

Step 1.1.2

Apply the distributive property.

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

Step 1.1.3

Apply the distributive property.

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

Step 1.2

Simplify and combine like terms.

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Step 1.2.1

Simplify each term.

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Step 1.2.1.1

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

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Step 1.2.1.1.1

Move $x$ .

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

Step 1.2.1.1.2

Multiply $x$ by $x$ .

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

Step 1.2.1.2

Multiply $4$ by $5$ .

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

Step 1.2.1.3

Multiply $- 3$ by $4$ .

$5 x^{2} + 20 x - 3 x - 12 - (2 x + 5) (3 x - 4)$

Step 1.2.2

Subtract $3 x$ from $20 x$ .

$5 x^{2} + 17 x - 12 - (2 x + 5) (3 x - 4)$

Step 1.3

Apply the distributive property.

$5 x^{2} + 17 x - 12 + (- (2 x) - 1 \cdot 5) (3 x - 4)$

Step 1.4

Multiply $2$ by $- 1$ .

$5 x^{2} + 17 x - 12 + (- 2 x - 1 \cdot 5) (3 x - 4)$

Step 1.5

Multiply $- 1$ by $5$ .

$5 x^{2} + 17 x - 12 + (- 2 x - 5) (3 x - 4)$

Step 1.6

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

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Step 1.6.1

Apply the distributive property.

$5 x^{2} + 17 x - 12 - 2 x (3 x - 4) - 5 (3 x - 4)$

Step 1.6.2

Apply the distributive property.

$5 x^{2} + 17 x - 12 - 2 x (3 x) - 2 x \cdot - 4 - 5 (3 x - 4)$

Step 1.6.3

Apply the distributive property.

$5 x^{2} + 17 x - 12 - 2 x (3 x) - 2 x \cdot - 4 - 5 (3 x) - 5 \cdot - 4$

Step 1.7

Simplify and combine like terms.

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Step 1.7.1

Simplify each term.

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Step 1.7.1.1

Rewrite using the commutative property of multiplication.

$5 x^{2} + 17 x - 12 - 2 \cdot 3 x \cdot x - 2 x \cdot - 4 - 5 (3 x) - 5 \cdot - 4$

Step 1.7.1.2

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

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Step 1.7.1.2.1

Move $x$ .

$5 x^{2} + 17 x - 12 - 2 \cdot 3 (x \cdot x) - 2 x \cdot - 4 - 5 (3 x) - 5 \cdot - 4$

Step 1.7.1.2.2

Multiply $x$ by $x$ .

$5 x^{2} + 17 x - 12 - 2 \cdot 3 x^{2} - 2 x \cdot - 4 - 5 (3 x) - 5 \cdot - 4$

Step 1.7.1.3

Multiply $- 2$ by $3$ .

$5 x^{2} + 17 x - 12 - 6 x^{2} - 2 x \cdot - 4 - 5 (3 x) - 5 \cdot - 4$

Step 1.7.1.4

Multiply $- 4$ by $- 2$ .

$5 x^{2} + 17 x - 12 - 6 x^{2} + 8 x - 5 (3 x) - 5 \cdot - 4$

Step 1.7.1.5

Multiply $3$ by $- 5$ .

$5 x^{2} + 17 x - 12 - 6 x^{2} + 8 x - 15 x - 5 \cdot - 4$

Step 1.7.1.6

Multiply $- 5$ by $- 4$ .

$5 x^{2} + 17 x - 12 - 6 x^{2} + 8 x - 15 x + 20$

Step 1.7.2

Subtract $15 x$ from $8 x$ .

$5 x^{2} + 17 x - 12 - 6 x^{2} - 7 x + 20$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $6 x^{2}$ from $5 x^{2}$ .

$- x^{2} + 17 x - 12 - 7 x + 20$

Step 2.2

Subtract $7 x$ from $17 x$ .

$- x^{2} + 10 x - 12 + 20$

Step 2.3

Add $- 12$ and $20$ .

$- x^{2} + 10 x + 8$