Algebra Examples

$4 \sqrt{12 x} - 5 \sqrt{32 y} - 4 \sqrt{48 x} + 8 \sqrt{50 y}$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Rewrite $12 x$ as $2^{2} \cdot (3 x)$ .

Tap for more steps...

Step 1.1.1

Factor $4$ out of $12$ .

$4 \sqrt{4 (3) x} - 5 \sqrt{32 y} - 4 \sqrt{48 x} + 8 \sqrt{50 y}$

Step 1.1.2

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

$4 \sqrt{2^{2} \cdot 3 x} - 5 \sqrt{32 y} - 4 \sqrt{48 x} + 8 \sqrt{50 y}$

Step 1.1.3

Add parentheses.

$4 \sqrt{2^{2} \cdot (3 x)} - 5 \sqrt{32 y} - 4 \sqrt{48 x} + 8 \sqrt{50 y}$

Step 1.2

Pull terms out from under the radical.

$4 (2 \sqrt{3 x}) - 5 \sqrt{32 y} - 4 \sqrt{48 x} + 8 \sqrt{50 y}$

Step 1.3

Multiply $2$ by $4$ .

$8 \sqrt{3 x} - 5 \sqrt{32 y} - 4 \sqrt{48 x} + 8 \sqrt{50 y}$

Step 1.4

Rewrite $32 y$ as ${(2^{2})}^{2} \cdot (2 y)$ .

Tap for more steps...

Step 1.4.1

Factor $16$ out of $32$ .

$8 \sqrt{3 x} - 5 \sqrt{16 (2) y} - 4 \sqrt{48 x} + 8 \sqrt{50 y}$

Step 1.4.2

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

$8 \sqrt{3 x} - 5 \sqrt{4^{2} \cdot 2 y} - 4 \sqrt{48 x} + 8 \sqrt{50 y}$

Step 1.4.3

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

$8 \sqrt{3 x} - 5 \sqrt{{(2^{2})}^{2} \cdot 2 y} - 4 \sqrt{48 x} + 8 \sqrt{50 y}$

Step 1.4.4

Add parentheses.

$8 \sqrt{3 x} - 5 \sqrt{{(2^{2})}^{2} \cdot (2 y)} - 4 \sqrt{48 x} + 8 \sqrt{50 y}$

Step 1.5

Pull terms out from under the radical.

$8 \sqrt{3 x} - 5 (2^{2} \sqrt{2 y}) - 4 \sqrt{48 x} + 8 \sqrt{50 y}$

Step 1.6

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

$8 \sqrt{3 x} - 5 (4 \sqrt{2 y}) - 4 \sqrt{48 x} + 8 \sqrt{50 y}$

Step 1.7

Multiply $4$ by $- 5$ .

$8 \sqrt{3 x} - 20 \sqrt{2 y} - 4 \sqrt{48 x} + 8 \sqrt{50 y}$

Step 1.8

Rewrite $48 x$ as ${(2^{2})}^{2} \cdot (3 x)$ .

Tap for more steps...

Step 1.8.1

Factor $16$ out of $48$ .

$8 \sqrt{3 x} - 20 \sqrt{2 y} - 4 \sqrt{16 (3) x} + 8 \sqrt{50 y}$

Step 1.8.2

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

$8 \sqrt{3 x} - 20 \sqrt{2 y} - 4 \sqrt{4^{2} \cdot 3 x} + 8 \sqrt{50 y}$

Step 1.8.3

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

$8 \sqrt{3 x} - 20 \sqrt{2 y} - 4 \sqrt{{(2^{2})}^{2} \cdot 3 x} + 8 \sqrt{50 y}$

Step 1.8.4

Add parentheses.

$8 \sqrt{3 x} - 20 \sqrt{2 y} - 4 \sqrt{{(2^{2})}^{2} \cdot (3 x)} + 8 \sqrt{50 y}$

Step 1.9

Pull terms out from under the radical.

$8 \sqrt{3 x} - 20 \sqrt{2 y} - 4 (2^{2} \sqrt{3 x}) + 8 \sqrt{50 y}$

Step 1.10

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

$8 \sqrt{3 x} - 20 \sqrt{2 y} - 4 (4 \sqrt{3 x}) + 8 \sqrt{50 y}$

Step 1.11

Multiply $4$ by $- 4$ .

$8 \sqrt{3 x} - 20 \sqrt{2 y} - 16 \sqrt{3 x} + 8 \sqrt{50 y}$

Step 1.12

Rewrite $50 y$ as $5^{2} \cdot (2 y)$ .

Tap for more steps...

Step 1.12.1

Factor $25$ out of $50$ .

$8 \sqrt{3 x} - 20 \sqrt{2 y} - 16 \sqrt{3 x} + 8 \sqrt{25 (2) y}$

Step 1.12.2

Rewrite $25$ as $5^{2}$ .

$8 \sqrt{3 x} - 20 \sqrt{2 y} - 16 \sqrt{3 x} + 8 \sqrt{5^{2} \cdot 2 y}$

Step 1.12.3

Add parentheses.

$8 \sqrt{3 x} - 20 \sqrt{2 y} - 16 \sqrt{3 x} + 8 \sqrt{5^{2} \cdot (2 y)}$

Step 1.13

Pull terms out from under the radical.

$8 \sqrt{3 x} - 20 \sqrt{2 y} - 16 \sqrt{3 x} + 8 (5 \sqrt{2 y})$

Step 1.14

Multiply $5$ by $8$ .

$8 \sqrt{3 x} - 20 \sqrt{2 y} - 16 \sqrt{3 x} + 40 \sqrt{2 y}$

Step 2

Simplify by adding terms.

Tap for more steps...

Step 2.1

Subtract $16 \sqrt{3 x}$ from $8 \sqrt{3 x}$ .

$- 8 \sqrt{3 x} - 20 \sqrt{2 y} + 40 \sqrt{2 y}$

Step 2.2

Add $- 20 \sqrt{2 y}$ and $40 \sqrt{2 y}$ .

$- 8 \sqrt{3 x} + 20 \sqrt{2 y}$