Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Multiply $2$ by $5$ .

$10 x + 5 x (- 3 x) + 4 (2 - 3 x) + 2 - 3 x$

Step 1.3

Rewrite using the commutative property of multiplication.

$10 x + 5 \cdot - 3 x \cdot x + 4 (2 - 3 x) + 2 - 3 x$

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 $x$ .

$10 x + 5 \cdot - 3 (x \cdot x) + 4 (2 - 3 x) + 2 - 3 x$

Step 1.4.1.2

Multiply $x$ by $x$ .

$10 x + 5 \cdot - 3 x^{2} + 4 (2 - 3 x) + 2 - 3 x$

Step 1.4.2

Multiply $5$ by $- 3$ .

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

Step 1.5

Apply the distributive property.

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

Step 1.6

Multiply $4$ by $2$ .

$10 x - 15 x^{2} + 8 + 4 (- 3 x) + 2 - 3 x$

Step 1.7

Multiply $- 3$ by $4$ .

$10 x - 15 x^{2} + 8 - 12 x + 2 - 3 x$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $12 x$ from $10 x$ .

$- 2 x - 15 x^{2} + 8 + 2 - 3 x$

Step 2.2

Subtract $3 x$ from $- 2 x$ .

$- 5 x - 15 x^{2} + 8 + 2$

Step 2.3

Simplify the expression.

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Step 2.3.1

Add $8$ and $2$ .

$- 5 x - 15 x^{2} + 10$

Step 2.3.2

Reorder $- 5 x$ and $- 15 x^{2}$ .

$- 15 x^{2} - 5 x + 10$