Simplify -7x^2 square root of 40x^3-8 square root of 40x^7

$- 7 x^{2} \sqrt{40 x^{3}} - 8 \sqrt{40 x^{7}}$

Step 1

Simplify each term.

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

Factor $4$ out of $40$ .

$- 7 x^{2} \sqrt{4 (10) x^{3}} - 8 \sqrt{40 x^{7}}$

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

$- 7 x^{2} \sqrt{2^{2} \cdot 10 x^{3}} - 8 \sqrt{40 x^{7}}$

Factor out $x^{2}$ .

$- 7 x^{2} \sqrt{2^{2} \cdot 10 (x^{2} x)} - 8 \sqrt{40 x^{7}}$

Move $10$ .

$- 7 x^{2} \sqrt{2^{2} x^{2} \cdot 10 x} - 8 \sqrt{40 x^{7}}$

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

$- 7 x^{2} \sqrt{{(2 x)}^{2} \cdot 10 x} - 8 \sqrt{40 x^{7}}$

Add parentheses.

$- 7 x^{2} \sqrt{{(2 x)}^{2} \cdot (10 x)} - 8 \sqrt{40 x^{7}}$

Pull terms out from under the radical.

$- 7 x^{2} (2 x \sqrt{10 x}) - 8 \sqrt{40 x^{7}}$

Multiply $x^{2}$ by $x$ by adding the exponents.

Move $x$ .

$- 7 (x \cdot x^{2}) (2 \sqrt{10 x}) - 8 \sqrt{40 x^{7}}$

Multiply $x$ by $x^{2}$ .

Raise $x$ to the power of $1$ .

$- 7 (x^{1} x^{2}) (2 \sqrt{10 x}) - 8 \sqrt{40 x^{7}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- 7 x^{1 + 2} (2 \sqrt{10 x}) - 8 \sqrt{40 x^{7}}$

Add $1$ and $2$ .

$- 7 x^{3} (2 \sqrt{10 x}) - 8 \sqrt{40 x^{7}}$

Multiply $2$ by $- 7$ .

$- 14 x^{3} \sqrt{10 x} - 8 \sqrt{40 x^{7}}$

Rewrite $40 x^{7}$ as ${(2 x^{3})}^{2} \cdot (10 x)$ .

Factor $4$ out of $40$ .

$- 14 x^{3} \sqrt{10 x} - 8 \sqrt{4 (10) x^{7}}$

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

$- 14 x^{3} \sqrt{10 x} - 8 \sqrt{2^{2} \cdot 10 x^{7}}$

Factor out $x^{6}$ .

$- 14 x^{3} \sqrt{10 x} - 8 \sqrt{2^{2} \cdot 10 (x^{6} x)}$

Rewrite $x^{6}$ as ${(x^{3})}^{2}$ .

$- 14 x^{3} \sqrt{10 x} - 8 \sqrt{2^{2} \cdot 10 ({(x^{3})}^{2} x)}$

Move $10$ .

$- 14 x^{3} \sqrt{10 x} - 8 \sqrt{2^{2} {(x^{3})}^{2} \cdot 10 x}$

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

$- 14 x^{3} \sqrt{10 x} - 8 \sqrt{{(2 x^{3})}^{2} \cdot 10 x}$

Add parentheses.

$- 14 x^{3} \sqrt{10 x} - 8 \sqrt{{(2 x^{3})}^{2} \cdot (10 x)}$

Pull terms out from under the radical.

$- 14 x^{3} \sqrt{10 x} - 8 (2 x^{3} \sqrt{10 x})$

Multiply $2$ by $- 8$ .

$- 14 x^{3} \sqrt{10 x} - 16 x^{3} \sqrt{10 x}$

Step 2

Subtract $16 x^{3} \sqrt{10 x}$ from $- 14 x^{3} \sqrt{10 x}$ .

$- 30 x^{3} \sqrt{10 x}$

Simplify -7x^2 square root of 40x^3-8 square root of 40x^7

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