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

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

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

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

Multiply $2$ by $3$ .

$6 \sqrt{y} \sqrt{y} + 3 \sqrt{y} (5 \sqrt{5}) - \sqrt{5} (2 \sqrt{y}) - \sqrt{5} (5 \sqrt{5})$

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

$6 ({\sqrt{y}}^{1} \sqrt{y}) + 3 \sqrt{y} (5 \sqrt{5}) - \sqrt{5} (2 \sqrt{y}) - \sqrt{5} (5 \sqrt{5})$

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

$6 ({\sqrt{y}}^{1} {\sqrt{y}}^{1}) + 3 \sqrt{y} (5 \sqrt{5}) - \sqrt{5} (2 \sqrt{y}) - \sqrt{5} (5 \sqrt{5})$

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

$6 {\sqrt{y}}^{1 + 1} + 3 \sqrt{y} (5 \sqrt{5}) - \sqrt{5} (2 \sqrt{y}) - \sqrt{5} (5 \sqrt{5})$

Add $1$ and $1$ .

$6 {\sqrt{y}}^{2} + 3 \sqrt{y} (5 \sqrt{5}) - \sqrt{5} (2 \sqrt{y}) - \sqrt{5} (5 \sqrt{5})$

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

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

$6 {(y^{\frac{1}{2}})}^{2} + 3 \sqrt{y} (5 \sqrt{5}) - \sqrt{5} (2 \sqrt{y}) - \sqrt{5} (5 \sqrt{5})$

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

$6 y^{\frac{1}{2} \cdot 2} + 3 \sqrt{y} (5 \sqrt{5}) - \sqrt{5} (2 \sqrt{y}) - \sqrt{5} (5 \sqrt{5})$

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

$6 y^{\frac{2}{2}} + 3 \sqrt{y} (5 \sqrt{5}) - \sqrt{5} (2 \sqrt{y}) - \sqrt{5} (5 \sqrt{5})$

Cancel the common factor of $2$ .

Cancel the common factor.

$6 y^{\frac{2}{2}} + 3 \sqrt{y} (5 \sqrt{5}) - \sqrt{5} (2 \sqrt{y}) - \sqrt{5} (5 \sqrt{5})$

Rewrite the expression.

$6 y^{1} + 3 \sqrt{y} (5 \sqrt{5}) - \sqrt{5} (2 \sqrt{y}) - \sqrt{5} (5 \sqrt{5})$

Simplify.

$6 y + 3 \sqrt{y} (5 \sqrt{5}) - \sqrt{5} (2 \sqrt{y}) - \sqrt{5} (5 \sqrt{5})$

Multiply $3 \sqrt{y} (5 \sqrt{5})$ .

Multiply $5$ by $3$ .

$6 y + 15 \sqrt{y} \sqrt{5} - \sqrt{5} (2 \sqrt{y}) - \sqrt{5} (5 \sqrt{5})$

Combine using the product rule for radicals.

$6 y + 15 \sqrt{5 y} - \sqrt{5} (2 \sqrt{y}) - \sqrt{5} (5 \sqrt{5})$

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

Multiply $2$ by $- 1$ .

$6 y + 15 \sqrt{5 y} - 2 \sqrt{5} \sqrt{y} - \sqrt{5} (5 \sqrt{5})$

Combine using the product rule for radicals.

$6 y + 15 \sqrt{5 y} - 2 \sqrt{y \cdot 5} - \sqrt{5} (5 \sqrt{5})$

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

Multiply $5$ by $- 1$ .

$6 y + 15 \sqrt{5 y} - 2 \sqrt{y \cdot 5} - 5 \sqrt{5} \sqrt{5}$

Raise $\sqrt{5}$ to the power of $1$ .

$6 y + 15 \sqrt{5 y} - 2 \sqrt{y \cdot 5} - 5 ({\sqrt{5}}^{1} \sqrt{5})$

Raise $\sqrt{5}$ to the power of $1$ .

$6 y + 15 \sqrt{5 y} - 2 \sqrt{y \cdot 5} - 5 ({\sqrt{5}}^{1} {\sqrt{5}}^{1})$

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

$6 y + 15 \sqrt{5 y} - 2 \sqrt{y \cdot 5} - 5 {\sqrt{5}}^{1 + 1}$

Add $1$ and $1$ .

$6 y + 15 \sqrt{5 y} - 2 \sqrt{y \cdot 5} - 5 {\sqrt{5}}^{2}$

Rewrite ${\sqrt{5}}^{2}$ as $5$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5}$ as $5^{\frac{1}{2}}$ .

$6 y + 15 \sqrt{5 y} - 2 \sqrt{y \cdot 5} - 5 {(5^{\frac{1}{2}})}^{2}$

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

$6 y + 15 \sqrt{5 y} - 2 \sqrt{y \cdot 5} - 5 \cdot 5^{\frac{1}{2} \cdot 2}$

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

$6 y + 15 \sqrt{5 y} - 2 \sqrt{y \cdot 5} - 5 \cdot 5^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$6 y + 15 \sqrt{5 y} - 2 \sqrt{y \cdot 5} - 5 \cdot 5^{\frac{2}{2}}$

Rewrite the expression.

$6 y + 15 \sqrt{5 y} - 2 \sqrt{y \cdot 5} - 5 \cdot 5^{1}$

Evaluate the exponent.

$6 y + 15 \sqrt{5 y} - 2 \sqrt{y \cdot 5} - 5 \cdot 5$

Multiply $- 5$ by $5$ .

$6 y + 15 \sqrt{5 y} - 2 \sqrt{y \cdot 5} - 25$

Subtract $2 \sqrt{y \cdot 5}$ from $15 \sqrt{5 y}$ .

Reorder $y$ and $5$ .

$6 y + 15 \sqrt{5 y} - 2 \sqrt{5 \cdot y} - 25$

Subtract $2 \sqrt{5 \cdot y}$ from $15 \sqrt{5 y}$ .

$6 y + 13 \sqrt{5 y} - 25$

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

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