Simplify 4 square root of 50c^2-4 square root of 98c^2+4c square root of 72

$4 \sqrt{50 c^{2}} - 4 \sqrt{98 c^{2}} + 4 c \sqrt{72}$

Simplify each term.

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

Factor $25$ out of $50$ .

$4 \sqrt{25 (2) c^{2}} - 4 \sqrt{98 c^{2}} + 4 c \sqrt{72}$

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

$4 \sqrt{5^{2} \cdot 2 c^{2}} - 4 \sqrt{98 c^{2}} + 4 c \sqrt{72}$

Move $2$ .

$4 \sqrt{5^{2} c^{2} \cdot 2} - 4 \sqrt{98 c^{2}} + 4 c \sqrt{72}$

Rewrite $5^{2} c^{2}$ as ${(5 c)}^{2}$ .

$4 \sqrt{{(5 c)}^{2} \cdot 2} - 4 \sqrt{98 c^{2}} + 4 c \sqrt{72}$

Pull terms out from under the radical.

$4 (5 c \sqrt{2}) - 4 \sqrt{98 c^{2}} + 4 c \sqrt{72}$

Multiply $5$ by $4$ .

$20 (c \sqrt{2}) - 4 \sqrt{98 c^{2}} + 4 c \sqrt{72}$

Rewrite $98 c^{2}$ as ${(7 c)}^{2} \cdot 2$ .

Factor $49$ out of $98$ .

$20 c \sqrt{2} - 4 \sqrt{49 (2) c^{2}} + 4 c \sqrt{72}$

Rewrite $49$ as $7^{2}$ .

$20 c \sqrt{2} - 4 \sqrt{7^{2} \cdot 2 c^{2}} + 4 c \sqrt{72}$

Move $2$ .

$20 c \sqrt{2} - 4 \sqrt{7^{2} c^{2} \cdot 2} + 4 c \sqrt{72}$

Rewrite $7^{2} c^{2}$ as ${(7 c)}^{2}$ .

$20 c \sqrt{2} - 4 \sqrt{{(7 c)}^{2} \cdot 2} + 4 c \sqrt{72}$

Pull terms out from under the radical.

$20 c \sqrt{2} - 4 (7 c \sqrt{2}) + 4 c \sqrt{72}$

Multiply $7$ by $- 4$ .

$20 c \sqrt{2} - 28 (c \sqrt{2}) + 4 c \sqrt{72}$

Rewrite $72$ as $6^{2} \cdot 2$ .

Factor $36$ out of $72$ .

$20 c \sqrt{2} - 28 c \sqrt{2} + 4 c \sqrt{36 (2)}$

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

$20 c \sqrt{2} - 28 c \sqrt{2} + 4 c \sqrt{6^{2} \cdot 2}$

Pull terms out from under the radical.

$20 c \sqrt{2} - 28 c \sqrt{2} + 4 c (6 \sqrt{2})$

Multiply $6$ by $4$ .

$20 c \sqrt{2} - 28 c \sqrt{2} + 24 c \sqrt{2}$

Simplify by adding terms.

Subtract $28 c \sqrt{2}$ from $20 c \sqrt{2}$ .

$- 8 c \sqrt{2} + 24 c \sqrt{2}$

Add $- 8 c \sqrt{2}$ and $24 c \sqrt{2}$ .

$16 c \sqrt{2}$