Algebra Examples

$\sqrt{144 {(x + 9)}^{10}}$

Step 1

Rewrite $144 {(x + 9)}^{10}$ as ${(12 {(x + 9)}^{5})}^{2}$ .

$\sqrt{{(12 {(x + 9)}^{5})}^{2}}$

Step 2

Pull terms out from under the radical.

$| 12 {(x + 9)}^{5} |$

Step 3

Use the Binomial Theorem.

$| 12 (x^{5} + 5 x^{4} \cdot 9 + 10 x^{3} \cdot 9^{2} + 10 x^{2} \cdot 9^{3} + 5 x \cdot 9^{4} + 9^{5}) |$

Step 4

Simplify each term.

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Step 4.1

Multiply $9$ by $5$ .

$| 12 (x^{5} + 45 x^{4} + 10 x^{3} \cdot 9^{2} + 10 x^{2} \cdot 9^{3} + 5 x \cdot 9^{4} + 9^{5}) |$

Step 4.2

Raise $9$ to the power of $2$ .

$| 12 (x^{5} + 45 x^{4} + 10 x^{3} \cdot 81 + 10 x^{2} \cdot 9^{3} + 5 x \cdot 9^{4} + 9^{5}) |$

Step 4.3

Multiply $81$ by $10$ .

$| 12 (x^{5} + 45 x^{4} + 810 x^{3} + 10 x^{2} \cdot 9^{3} + 5 x \cdot 9^{4} + 9^{5}) |$

Step 4.4

Raise $9$ to the power of $3$ .

$| 12 (x^{5} + 45 x^{4} + 810 x^{3} + 10 x^{2} \cdot 729 + 5 x \cdot 9^{4} + 9^{5}) |$

Step 4.5

Multiply $729$ by $10$ .

$| 12 (x^{5} + 45 x^{4} + 810 x^{3} + 7290 x^{2} + 5 x \cdot 9^{4} + 9^{5}) |$

Step 4.6

Raise $9$ to the power of $4$ .

$| 12 (x^{5} + 45 x^{4} + 810 x^{3} + 7290 x^{2} + 5 x \cdot 6561 + 9^{5}) |$

Step 4.7

Multiply $6561$ by $5$ .

$| 12 (x^{5} + 45 x^{4} + 810 x^{3} + 7290 x^{2} + 32805 x + 9^{5}) |$

Step 4.8

Raise $9$ to the power of $5$ .

$| 12 (x^{5} + 45 x^{4} + 810 x^{3} + 7290 x^{2} + 32805 x + 59049) |$

Step 5

Apply the distributive property.

$| 12 x^{5} + 12 (45 x^{4}) + 12 (810 x^{3}) + 12 (7290 x^{2}) + 12 (32805 x) + 12 \cdot 59049 |$

Step 6

Simplify.

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Step 6.1

Multiply $45$ by $12$ .

$| 12 x^{5} + 540 x^{4} + 12 (810 x^{3}) + 12 (7290 x^{2}) + 12 (32805 x) + 12 \cdot 59049 |$

Step 6.2

Multiply $810$ by $12$ .

$| 12 x^{5} + 540 x^{4} + 9720 x^{3} + 12 (7290 x^{2}) + 12 (32805 x) + 12 \cdot 59049 |$

Step 6.3

Multiply $7290$ by $12$ .

$| 12 x^{5} + 540 x^{4} + 9720 x^{3} + 87480 x^{2} + 12 (32805 x) + 12 \cdot 59049 |$

Step 6.4

Multiply $32805$ by $12$ .

$| 12 x^{5} + 540 x^{4} + 9720 x^{3} + 87480 x^{2} + 393660 x + 12 \cdot 59049 |$

Step 6.5

Multiply $12$ by $59049$ .

$| 12 x^{5} + 540 x^{4} + 9720 x^{3} + 87480 x^{2} + 393660 x + 708588 |$