Basic Math Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Apply the distributive property.

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

Step 1.1.2

Apply the distributive property.

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

Step 1.1.3

Apply the distributive property.

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

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

Rewrite using the commutative property of multiplication.

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

Step 1.2.1.2

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

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Step 1.2.1.2.1

Move $x$ .

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

Step 1.2.1.2.2

Multiply $x$ by $x$ .

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

Step 1.2.1.3

Multiply $5$ by $3$ .

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

Step 1.2.1.4

Multiply $- 2$ by $5$ .

$15 x^{2} - 10 x + 4 (3 x) + 4 \cdot - 2 - 4 (2 x + 1)$

Step 1.2.1.5

Multiply $3$ by $4$ .

$15 x^{2} - 10 x + 12 x + 4 \cdot - 2 - 4 (2 x + 1)$

Step 1.2.1.6

Multiply $4$ by $- 2$ .

$15 x^{2} - 10 x + 12 x - 8 - 4 (2 x + 1)$

Step 1.2.2

Add $- 10 x$ and $12 x$ .

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

Step 1.3

Apply the distributive property.

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

Step 1.4

Multiply $2$ by $- 4$ .

$15 x^{2} + 2 x - 8 - 8 x - 4 \cdot 1$

Step 1.5

Multiply $- 4$ by $1$ .

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

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $8 x$ from $2 x$ .

$15 x^{2} - 6 x - 8 - 4$

Step 2.2

Subtract $4$ from $- 8$ .

$15 x^{2} - 6 x - 12$