Algebra Examples

$3 (5 x^{2} + 2 x - 4) - x (7 x^{2} + 2 x - 3)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$3 (5 x^{2}) + 3 (2 x) + 3 \cdot - 4 - x (7 x^{2} + 2 x - 3)$

Step 1.2

Simplify.

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Step 1.2.1

Multiply $5$ by $3$ .

$15 x^{2} + 3 (2 x) + 3 \cdot - 4 - x (7 x^{2} + 2 x - 3)$

Step 1.2.2

Multiply $2$ by $3$ .

$15 x^{2} + 6 x + 3 \cdot - 4 - x (7 x^{2} + 2 x - 3)$

Step 1.2.3

Multiply $3$ by $- 4$ .

$15 x^{2} + 6 x - 12 - x (7 x^{2} + 2 x - 3)$

Step 1.3

Apply the distributive property.

$15 x^{2} + 6 x - 12 - x (7 x^{2}) - x (2 x) - x \cdot - 3$

Step 1.4

Simplify.

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Step 1.4.1

Rewrite using the commutative property of multiplication.

$15 x^{2} + 6 x - 12 - 1 \cdot 7 x \cdot x^{2} - x (2 x) - x \cdot - 3$

Step 1.4.2

Rewrite using the commutative property of multiplication.

$15 x^{2} + 6 x - 12 - 1 \cdot 7 x \cdot x^{2} - 1 \cdot 2 x \cdot x - x \cdot - 3$

Step 1.4.3

Multiply $- 3$ by $- 1$ .

$15 x^{2} + 6 x - 12 - 1 \cdot 7 x \cdot x^{2} - 1 \cdot 2 x \cdot x + 3 x$

Step 1.5

Simplify each term.

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Step 1.5.1

Multiply $x$ by $x^{2}$ by adding the exponents.

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Step 1.5.1.1

Move $x^{2}$ .

$15 x^{2} + 6 x - 12 - 1 \cdot 7 (x^{2} x) - 1 \cdot 2 x \cdot x + 3 x$

Step 1.5.1.2

Multiply $x^{2}$ by $x$ .

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Step 1.5.1.2.1

Raise $x$ to the power of $1$ .

$15 x^{2} + 6 x - 12 - 1 \cdot 7 (x^{2} x^{1}) - 1 \cdot 2 x \cdot x + 3 x$

Step 1.5.1.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$15 x^{2} + 6 x - 12 - 1 \cdot 7 x^{2 + 1} - 1 \cdot 2 x \cdot x + 3 x$

Step 1.5.1.3

Add $2$ and $1$ .

$15 x^{2} + 6 x - 12 - 1 \cdot 7 x^{3} - 1 \cdot 2 x \cdot x + 3 x$

Step 1.5.2

Multiply $- 1$ by $7$ .

$15 x^{2} + 6 x - 12 - 7 x^{3} - 1 \cdot 2 x \cdot x + 3 x$

Step 1.5.3

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

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Step 1.5.3.1

Move $x$ .

$15 x^{2} + 6 x - 12 - 7 x^{3} - 1 \cdot 2 (x \cdot x) + 3 x$

Step 1.5.3.2

Multiply $x$ by $x$ .

$15 x^{2} + 6 x - 12 - 7 x^{3} - 1 \cdot 2 x^{2} + 3 x$

Step 1.5.4

Multiply $- 1$ by $2$ .

$15 x^{2} + 6 x - 12 - 7 x^{3} - 2 x^{2} + 3 x$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $2 x^{2}$ from $15 x^{2}$ .

$13 x^{2} + 6 x - 12 - 7 x^{3} + 3 x$

Step 2.2

Add $6 x$ and $3 x$ .

$13 x^{2} + 9 x - 12 - 7 x^{3}$

Step 2.3

Simplify the expression.

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Step 2.3.1

Move $- 12$ .

$13 x^{2} + 9 x - 7 x^{3} - 12$

Step 2.3.2

Move $9 x$ .

$13 x^{2} - 7 x^{3} + 9 x - 12$

Step 2.3.3

Reorder $13 x^{2}$ and $- 7 x^{3}$ .

$- 7 x^{3} + 13 x^{2} + 9 x - 12$