Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Rewrite using the commutative property of multiplication.

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

Step 1.3

Rewrite using the commutative property of multiplication.

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

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 $x$ .

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

Step 1.4.1.2

Multiply $x$ by $x$ .

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

Step 1.4.2

Multiply $a$ by $a$ by adding the exponents.

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Step 1.4.2.1

Move $a$ .

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

Step 1.4.2.2

Multiply $a$ by $a$ .

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

Step 1.5

Apply the distributive property.

$2 a x^{2} - 3 a^{2} x - x (a x) - x (5 a^{2})$

Step 1.6

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

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Step 1.6.1

Move $x$ .

$2 a x^{2} - 3 a^{2} x - (x \cdot x) a - x (5 a^{2})$

Step 1.6.2

Multiply $x$ by $x$ .

$2 a x^{2} - 3 a^{2} x - x^{2} a - x (5 a^{2})$

Step 1.7

Rewrite using the commutative property of multiplication.

$2 a x^{2} - 3 a^{2} x - x^{2} a - 1 \cdot 5 x a^{2}$

Step 1.8

Multiply $- 1$ by $5$ .

$2 a x^{2} - 3 a^{2} x - x^{2} a - 5 x a^{2}$

Step 2

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

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Step 2.1

Move $x^{2}$ .

$2 a x^{2} - 1 a x^{2} - 3 a^{2} x - 5 x a^{2}$

Step 2.2

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

$1 a x^{2} - 3 a^{2} x - 5 x a^{2}$

Step 3

Multiply $a$ by $1$ .

$a x^{2} - 3 a^{2} x - 5 x a^{2}$

Step 4

Subtract $5 x a^{2}$ from $- 3 a^{2} x$ .

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Step 4.1

Move $x$ .

$a x^{2} - 3 a^{2} x - 5 a^{2} x$

Step 4.2

Subtract $5 a^{2} x$ from $- 3 a^{2} x$ .

$a x^{2} - 8 a^{2} x$