Algebra Examples

$3 \sqrt{40 a^{3}} + 2 \sqrt{160 a^{3}} - a \sqrt{360 a}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $40 a^{3}$ as ${(2 a)}^{2} \cdot (10 a)$ .

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Step 1.1.1

Factor $4$ out of $40$ .

$3 \sqrt{4 (10) a^{3}} + 2 \sqrt{160 a^{3}} - a \sqrt{360 a}$

Step 1.1.2

Rewrite $4$ as $2^{2}$ .

$3 \sqrt{2^{2} \cdot 10 a^{3}} + 2 \sqrt{160 a^{3}} - a \sqrt{360 a}$

Step 1.1.3

Factor out $a^{2}$ .

$3 \sqrt{2^{2} \cdot 10 (a^{2} a)} + 2 \sqrt{160 a^{3}} - a \sqrt{360 a}$

Step 1.1.4

Move $10$ .

$3 \sqrt{2^{2} a^{2} \cdot 10 a} + 2 \sqrt{160 a^{3}} - a \sqrt{360 a}$

Step 1.1.5

Rewrite $2^{2} a^{2}$ as ${(2 a)}^{2}$ .

$3 \sqrt{{(2 a)}^{2} \cdot 10 a} + 2 \sqrt{160 a^{3}} - a \sqrt{360 a}$

Step 1.1.6

Add parentheses.

$3 \sqrt{{(2 a)}^{2} \cdot (10 a)} + 2 \sqrt{160 a^{3}} - a \sqrt{360 a}$

Step 1.2

Pull terms out from under the radical.

$3 (2 a \sqrt{10 a}) + 2 \sqrt{160 a^{3}} - a \sqrt{360 a}$

Step 1.3

Multiply $2$ by $3$ .

$6 (a \sqrt{10 a}) + 2 \sqrt{160 a^{3}} - a \sqrt{360 a}$

Step 1.4

Rewrite $160 a^{3}$ as ${(4 a)}^{2} \cdot (10 a)$ .

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Step 1.4.1

Factor $16$ out of $160$ .

$6 a \sqrt{10 a} + 2 \sqrt{16 (10) a^{3}} - a \sqrt{360 a}$

Step 1.4.2

Rewrite $16$ as $4^{2}$ .

$6 a \sqrt{10 a} + 2 \sqrt{4^{2} \cdot 10 a^{3}} - a \sqrt{360 a}$

Step 1.4.3

Factor out $a^{2}$ .

$6 a \sqrt{10 a} + 2 \sqrt{4^{2} \cdot 10 (a^{2} a)} - a \sqrt{360 a}$

Step 1.4.4

Move $10$ .

$6 a \sqrt{10 a} + 2 \sqrt{4^{2} a^{2} \cdot 10 a} - a \sqrt{360 a}$

Step 1.4.5

Rewrite $4^{2} a^{2}$ as ${(4 a)}^{2}$ .

$6 a \sqrt{10 a} + 2 \sqrt{{(4 a)}^{2} \cdot 10 a} - a \sqrt{360 a}$

Step 1.4.6

Add parentheses.

$6 a \sqrt{10 a} + 2 \sqrt{{(4 a)}^{2} \cdot (10 a)} - a \sqrt{360 a}$

Step 1.5

Pull terms out from under the radical.

$6 a \sqrt{10 a} + 2 (4 a \sqrt{10 a}) - a \sqrt{360 a}$

Step 1.6

Multiply $4$ by $2$ .

$6 a \sqrt{10 a} + 8 (a \sqrt{10 a}) - a \sqrt{360 a}$

Step 1.7

Rewrite $360 a$ as $6^{2} \cdot (10 a)$ .

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Step 1.7.1

Factor $36$ out of $360$ .

$6 a \sqrt{10 a} + 8 a \sqrt{10 a} - a \sqrt{36 (10) a}$

Step 1.7.2

Rewrite $36$ as $6^{2}$ .

$6 a \sqrt{10 a} + 8 a \sqrt{10 a} - a \sqrt{6^{2} \cdot 10 a}$

Step 1.7.3

Add parentheses.

$6 a \sqrt{10 a} + 8 a \sqrt{10 a} - a \sqrt{6^{2} \cdot (10 a)}$

Step 1.8

Pull terms out from under the radical.

$6 a \sqrt{10 a} + 8 a \sqrt{10 a} - a (6 \sqrt{10 a})$

Step 1.9

Multiply $6$ by $- 1$ .

$6 a \sqrt{10 a} + 8 a \sqrt{10 a} - 6 a \sqrt{10 a}$

Step 2

Combine the opposite terms in $6 a \sqrt{10 a} + 8 a \sqrt{10 a} - 6 a \sqrt{10 a}$ .

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Step 2.1

Subtract $6 a \sqrt{10 a}$ from $6 a \sqrt{10 a}$ .

$8 a \sqrt{10 a} + 0$

Step 2.2

Add $8 a \sqrt{10 a}$ and $0$ .

$8 a \sqrt{10 a}$