Basic Math Examples

$3 \cdot a \cdot b \cdot a = b \cdot a \cdot a$

Step 1

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

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Step 1.1

Move $a$ .

$3 \cdot (a \cdot a) \cdot b = b \cdot a \cdot a$

Step 1.2

Multiply $a$ by $a$ .

$3 \cdot a^{2} \cdot b = b \cdot a \cdot a$

$3 a^{2} b = b \cdot a \cdot a$

Step 2

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

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Step 2.1

Move $a$ .

$3 a^{2} b = b \cdot (a \cdot a)$

Step 2.2

Multiply $a$ by $a$ .

$3 a^{2} b = b \cdot a^{2}$

$3 a^{2} b = b a^{2}$

Step 3

Move all terms containing $a$ to the left side of the equation.

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Step 3.1

Subtract $b a^{2}$ from both sides of the equation.

$3 a^{2} b - b a^{2} = 0$

Step 3.2

Subtract $b a^{2}$ from $3 a^{2} b$ .

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Step 3.2.1

Move $b$ .

$3 a^{2} b - 1 a^{2} b = 0$

Step 3.2.2

Subtract $a^{2} b$ from $3 a^{2} b$ .

$2 a^{2} b = 0$

Step 4

Divide each term in $2 a^{2} b = 0$ by $2 b$ and simplify.

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Step 4.1

Divide each term in $2 a^{2} b = 0$ by $2 b$ .

$\frac{2 a^{2} b}{2 b} = \frac{0}{2 b}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $2$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{2 a^{2} b}{2 b} = \frac{0}{2 b}$

Step 4.2.1.2

Rewrite the expression.

$\frac{a^{2} b}{b} = \frac{0}{2 b}$

Step 4.2.2

Cancel the common factor of $b$ .

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Step 4.2.2.1

Cancel the common factor.

$\frac{a^{2} b}{b} = \frac{0}{2 b}$

Step 4.2.2.2

Divide $a^{2}$ by $1$ .

$a^{2} = \frac{0}{2 b}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Cancel the common factor of $0$ and $2$ .

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Step 4.3.1.1

Factor $2$ out of $0$ .

$a^{2} = \frac{2 (0)}{2 b}$

Step 4.3.1.2

Cancel the common factors.

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Step 4.3.1.2.1

Factor $2$ out of $2 b$ .

$a^{2} = \frac{2 (0)}{2 (b)}$

Step 4.3.1.2.2

Cancel the common factor.

$a^{2} = \frac{2 \cdot 0}{2 b}$

Step 4.3.1.2.3

Rewrite the expression.

$a^{2} = \frac{0}{b}$

Step 4.3.2

Divide $0$ by $b$ .

$a^{2} = 0$

Step 5

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$a = \pm \sqrt{0}$

Step 6

Simplify $\pm \sqrt{0}$ .

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Step 6.1

Rewrite $0$ as $0^{2}$ .

$a = \pm \sqrt{0^{2}}$

Step 6.2

Pull terms out from under the radical, assuming positive real numbers.

$a = \pm 0$

Step 6.3

Plus or minus $0$ is $0$ .

$a = 0$