Algebra Examples

$6 x (2 x - 3) - 5 (2 x^{2} + 9 x - 3)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$6 x (2 x) + 6 x \cdot - 3 - 5 (2 x^{2} + 9 x - 3)$

Step 1.2

Rewrite using the commutative property of multiplication.

$6 \cdot 2 x \cdot x + 6 x \cdot - 3 - 5 (2 x^{2} + 9 x - 3)$

Step 1.3

Multiply $- 3$ by $6$ .

$6 \cdot 2 x \cdot x - 18 x - 5 (2 x^{2} + 9 x - 3)$

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 $x$ .

$6 \cdot 2 (x \cdot x) - 18 x - 5 (2 x^{2} + 9 x - 3)$

Step 1.4.1.2

Multiply $x$ by $x$ .

$6 \cdot 2 x^{2} - 18 x - 5 (2 x^{2} + 9 x - 3)$

Step 1.4.2

Multiply $6$ by $2$ .

$12 x^{2} - 18 x - 5 (2 x^{2} + 9 x - 3)$

Step 1.5

Apply the distributive property.

$12 x^{2} - 18 x - 5 (2 x^{2}) - 5 (9 x) - 5 \cdot - 3$

Step 1.6

Simplify.

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Step 1.6.1

Multiply $2$ by $- 5$ .

$12 x^{2} - 18 x - 10 x^{2} - 5 (9 x) - 5 \cdot - 3$

Step 1.6.2

Multiply $9$ by $- 5$ .

$12 x^{2} - 18 x - 10 x^{2} - 45 x - 5 \cdot - 3$

Step 1.6.3

Multiply $- 5$ by $- 3$ .

$12 x^{2} - 18 x - 10 x^{2} - 45 x + 15$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $10 x^{2}$ from $12 x^{2}$ .

$2 x^{2} - 18 x - 45 x + 15$

Step 2.2

Subtract $45 x$ from $- 18 x$ .

$2 x^{2} - 63 x + 15$