Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Rewrite using the commutative property of multiplication.

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

Step 1.3

Multiply $5$ by $3$ .

$3 \cdot 4 x \cdot x + 15 x - 4 (- x - 3) (2 x - 5)$

Step 1.4

Simplify each term.

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Step 1.4.1

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

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Step 1.4.1.1

Move $x$ .

$3 \cdot 4 (x \cdot x) + 15 x - 4 (- x - 3) (2 x - 5)$

Step 1.4.1.2

Multiply $x$ by $x$ .

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

Step 1.4.2

Multiply $3$ by $4$ .

$12 x^{2} + 15 x - 4 (- x - 3) (2 x - 5)$

Step 1.5

Apply the distributive property.

$12 x^{2} + 15 x + (- 4 (- x) - 4 \cdot - 3) (2 x - 5)$

Step 1.6

Multiply $- 1$ by $- 4$ .

$12 x^{2} + 15 x + (4 x - 4 \cdot - 3) (2 x - 5)$

Step 1.7

Multiply $- 4$ by $- 3$ .

$12 x^{2} + 15 x + (4 x + 12) (2 x - 5)$

Step 1.8

Expand $(4 x + 12) (2 x - 5)$ using the FOIL Method.

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Step 1.8.1

Apply the distributive property.

$12 x^{2} + 15 x + 4 x (2 x - 5) + 12 (2 x - 5)$

Step 1.8.2

Apply the distributive property.

$12 x^{2} + 15 x + 4 x (2 x) + 4 x \cdot - 5 + 12 (2 x - 5)$

Step 1.8.3

Apply the distributive property.

$12 x^{2} + 15 x + 4 x (2 x) + 4 x \cdot - 5 + 12 (2 x) + 12 \cdot - 5$

Step 1.9

Simplify and combine like terms.

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Step 1.9.1

Simplify each term.

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Step 1.9.1.1

Rewrite using the commutative property of multiplication.

$12 x^{2} + 15 x + 4 \cdot 2 x \cdot x + 4 x \cdot - 5 + 12 (2 x) + 12 \cdot - 5$

Step 1.9.1.2

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

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Step 1.9.1.2.1

Move $x$ .

$12 x^{2} + 15 x + 4 \cdot 2 (x \cdot x) + 4 x \cdot - 5 + 12 (2 x) + 12 \cdot - 5$

Step 1.9.1.2.2

Multiply $x$ by $x$ .

$12 x^{2} + 15 x + 4 \cdot 2 x^{2} + 4 x \cdot - 5 + 12 (2 x) + 12 \cdot - 5$

Step 1.9.1.3

Multiply $4$ by $2$ .

$12 x^{2} + 15 x + 8 x^{2} + 4 x \cdot - 5 + 12 (2 x) + 12 \cdot - 5$

Step 1.9.1.4

Multiply $- 5$ by $4$ .

$12 x^{2} + 15 x + 8 x^{2} - 20 x + 12 (2 x) + 12 \cdot - 5$

Step 1.9.1.5

Multiply $2$ by $12$ .

$12 x^{2} + 15 x + 8 x^{2} - 20 x + 24 x + 12 \cdot - 5$

Step 1.9.1.6

Multiply $12$ by $- 5$ .

$12 x^{2} + 15 x + 8 x^{2} - 20 x + 24 x - 60$

Step 1.9.2

Add $- 20 x$ and $24 x$ .

$12 x^{2} + 15 x + 8 x^{2} + 4 x - 60$

Step 2

Simplify by adding terms.

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Step 2.1

Add $12 x^{2}$ and $8 x^{2}$ .

$20 x^{2} + 15 x + 4 x - 60$

Step 2.2

Add $15 x$ and $4 x$ .

$20 x^{2} + 19 x - 60$