Simplify (2 square root of y-3 square root of 2)(4 square root of y-5 square root of 2)

$(2 \sqrt{y} - 3 \sqrt{2}) (4 \sqrt{y} - 5 \sqrt{2})$

Expand $(2 \sqrt{y} - 3 \sqrt{2}) (4 \sqrt{y} - 5 \sqrt{2})$ using the FOIL Method.

Apply the distributive property.

$2 \sqrt{y} (4 \sqrt{y} - 5 \sqrt{2}) - 3 \sqrt{2} (4 \sqrt{y} - 5 \sqrt{2})$

Apply the distributive property.

$2 \sqrt{y} (4 \sqrt{y}) + 2 \sqrt{y} (- 5 \sqrt{2}) - 3 \sqrt{2} (4 \sqrt{y} - 5 \sqrt{2})$

Apply the distributive property.

$2 \sqrt{y} (4 \sqrt{y}) + 2 \sqrt{y} (- 5 \sqrt{2}) - 3 \sqrt{2} (4 \sqrt{y}) - 3 \sqrt{2} (- 5 \sqrt{2})$

Simplify and combine like terms.

Simplify each term.

Multiply $2 \sqrt{y} (4 \sqrt{y})$ .

Multiply $4$ by $2$ .

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

Raise $\sqrt{y}$ to the power of $1$ .

$8 ({\sqrt{y}}^{1} \sqrt{y}) + 2 \sqrt{y} (- 5 \sqrt{2}) - 3 \sqrt{2} (4 \sqrt{y}) - 3 \sqrt{2} (- 5 \sqrt{2})$

Raise $\sqrt{y}$ to the power of $1$ .

$8 ({\sqrt{y}}^{1} {\sqrt{y}}^{1}) + 2 \sqrt{y} (- 5 \sqrt{2}) - 3 \sqrt{2} (4 \sqrt{y}) - 3 \sqrt{2} (- 5 \sqrt{2})$

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

$8 {\sqrt{y}}^{1 + 1} + 2 \sqrt{y} (- 5 \sqrt{2}) - 3 \sqrt{2} (4 \sqrt{y}) - 3 \sqrt{2} (- 5 \sqrt{2})$

Add $1$ and $1$ .

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

Rewrite ${\sqrt{y}}^{2}$ as $y$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{y}$ as $y^{\frac{1}{2}}$ .

$8 {(y^{\frac{1}{2}})}^{2} + 2 \sqrt{y} (- 5 \sqrt{2}) - 3 \sqrt{2} (4 \sqrt{y}) - 3 \sqrt{2} (- 5 \sqrt{2})$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$8 y^{\frac{1}{2} \cdot 2} + 2 \sqrt{y} (- 5 \sqrt{2}) - 3 \sqrt{2} (4 \sqrt{y}) - 3 \sqrt{2} (- 5 \sqrt{2})$

Combine $\frac{1}{2}$ and $2$ .

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$8 y^{1} + 2 \sqrt{y} (- 5 \sqrt{2}) - 3 \sqrt{2} (4 \sqrt{y}) - 3 \sqrt{2} (- 5 \sqrt{2})$

Simplify.

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

Multiply $2 \sqrt{y} (- 5 \sqrt{2})$ .

Multiply $- 5$ by $2$ .

$8 y - 10 \sqrt{y} \sqrt{2} - 3 \sqrt{2} (4 \sqrt{y}) - 3 \sqrt{2} (- 5 \sqrt{2})$

Combine using the product rule for radicals.

$8 y - 10 \sqrt{2 y} - 3 \sqrt{2} (4 \sqrt{y}) - 3 \sqrt{2} (- 5 \sqrt{2})$

Multiply $- 3 \sqrt{2} (4 \sqrt{y})$ .

Multiply $4$ by $- 3$ .

$8 y - 10 \sqrt{2 y} - 12 \sqrt{2} \sqrt{y} - 3 \sqrt{2} (- 5 \sqrt{2})$

Combine using the product rule for radicals.

$8 y - 10 \sqrt{2 y} - 12 \sqrt{y \cdot 2} - 3 \sqrt{2} (- 5 \sqrt{2})$

Multiply $- 3 \sqrt{2} (- 5 \sqrt{2})$ .

Multiply $- 5$ by $- 3$ .

$8 y - 10 \sqrt{2 y} - 12 \sqrt{y \cdot 2} + 15 \sqrt{2} \sqrt{2}$

Raise $\sqrt{2}$ to the power of $1$ .

$8 y - 10 \sqrt{2 y} - 12 \sqrt{y \cdot 2} + 15 ({\sqrt{2}}^{1} \sqrt{2})$

Raise $\sqrt{2}$ to the power of $1$ .

$8 y - 10 \sqrt{2 y} - 12 \sqrt{y \cdot 2} + 15 ({\sqrt{2}}^{1} {\sqrt{2}}^{1})$

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

$8 y - 10 \sqrt{2 y} - 12 \sqrt{y \cdot 2} + 15 {\sqrt{2}}^{1 + 1}$

Add $1$ and $1$ .

$8 y - 10 \sqrt{2 y} - 12 \sqrt{y \cdot 2} + 15 {\sqrt{2}}^{2}$

Rewrite ${\sqrt{2}}^{2}$ as $2$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2}$ as $2^{\frac{1}{2}}$ .

$8 y - 10 \sqrt{2 y} - 12 \sqrt{y \cdot 2} + 15 {(2^{\frac{1}{2}})}^{2}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$8 y - 10 \sqrt{2 y} - 12 \sqrt{y \cdot 2} + 15 \cdot 2^{\frac{1}{2} \cdot 2}$

Combine $\frac{1}{2}$ and $2$ .

$8 y - 10 \sqrt{2 y} - 12 \sqrt{y \cdot 2} + 15 \cdot 2^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$8 y - 10 \sqrt{2 y} - 12 \sqrt{y \cdot 2} + 15 \cdot 2^{\frac{2}{2}}$

Rewrite the expression.

$8 y - 10 \sqrt{2 y} - 12 \sqrt{y \cdot 2} + 15 \cdot 2^{1}$

Evaluate the exponent.

$8 y - 10 \sqrt{2 y} - 12 \sqrt{y \cdot 2} + 15 \cdot 2$

Multiply $15$ by $2$ .

$8 y - 10 \sqrt{2 y} - 12 \sqrt{y \cdot 2} + 30$

Subtract $12 \sqrt{y \cdot 2}$ from $- 10 \sqrt{2 y}$ .

Reorder $y$ and $2$ .

$8 y - 10 \sqrt{2 y} - 12 \sqrt{2 \cdot y} + 30$

Subtract $12 \sqrt{2 \cdot y}$ from $- 10 \sqrt{2 y}$ .

$8 y - 22 \sqrt{2 y} + 30$

Simplify (2 square root of y-3 square root of 2)(4 square root of y-5 square root of 2)

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