Simplify ( square root of c- square root of d)^2

${(\sqrt{c} - \sqrt{d})}^{2}$

Step 1

Rewrite ${(\sqrt{c} - \sqrt{d})}^{2}$ as $(\sqrt{c} - \sqrt{d}) (\sqrt{c} - \sqrt{d})$ .

$(\sqrt{c} - \sqrt{d}) (\sqrt{c} - \sqrt{d})$

Step 2

Expand $(\sqrt{c} - \sqrt{d}) (\sqrt{c} - \sqrt{d})$ using the FOIL Method.

Apply the distributive property.

$\sqrt{c} (\sqrt{c} - \sqrt{d}) - \sqrt{d} (\sqrt{c} - \sqrt{d})$

Apply the distributive property.

$\sqrt{c} \sqrt{c} + \sqrt{c} (- \sqrt{d}) - \sqrt{d} (\sqrt{c} - \sqrt{d})$

Apply the distributive property.

$\sqrt{c} \sqrt{c} + \sqrt{c} (- \sqrt{d}) - \sqrt{d} \sqrt{c} - \sqrt{d} (- \sqrt{d})$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $\sqrt{c} \sqrt{c}$ .

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

${\sqrt{c}}^{1} \sqrt{c} + \sqrt{c} (- \sqrt{d}) - \sqrt{d} \sqrt{c} - \sqrt{d} (- \sqrt{d})$

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

${\sqrt{c}}^{1} {\sqrt{c}}^{1} + \sqrt{c} (- \sqrt{d}) - \sqrt{d} \sqrt{c} - \sqrt{d} (- \sqrt{d})$

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

${\sqrt{c}}^{1 + 1} + \sqrt{c} (- \sqrt{d}) - \sqrt{d} \sqrt{c} - \sqrt{d} (- \sqrt{d})$

Add $1$ and $1$ .

${\sqrt{c}}^{2} + \sqrt{c} (- \sqrt{d}) - \sqrt{d} \sqrt{c} - \sqrt{d} (- \sqrt{d})$

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

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

${(c^{\frac{1}{2}})}^{2} + \sqrt{c} (- \sqrt{d}) - \sqrt{d} \sqrt{c} - \sqrt{d} (- \sqrt{d})$

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

$c^{\frac{1}{2} \cdot 2} + \sqrt{c} (- \sqrt{d}) - \sqrt{d} \sqrt{c} - \sqrt{d} (- \sqrt{d})$

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

$c^{\frac{2}{2}} + \sqrt{c} (- \sqrt{d}) - \sqrt{d} \sqrt{c} - \sqrt{d} (- \sqrt{d})$

Cancel the common factor of $2$ .

Cancel the common factor.

$c^{\frac{2}{2}} + \sqrt{c} (- \sqrt{d}) - \sqrt{d} \sqrt{c} - \sqrt{d} (- \sqrt{d})$

Rewrite the expression.

$c^{1} + \sqrt{c} (- \sqrt{d}) - \sqrt{d} \sqrt{c} - \sqrt{d} (- \sqrt{d})$

Simplify.

$c + \sqrt{c} (- \sqrt{d}) - \sqrt{d} \sqrt{c} - \sqrt{d} (- \sqrt{d})$

Rewrite using the commutative property of multiplication.

$c - \sqrt{c} \sqrt{d} - \sqrt{d} \sqrt{c} - \sqrt{d} (- \sqrt{d})$

Combine using the product rule for radicals.

$c - \sqrt{d c} - \sqrt{d} \sqrt{c} - \sqrt{d} (- \sqrt{d})$

Combine using the product rule for radicals.

$c - \sqrt{d c} - \sqrt{c d} - \sqrt{d} (- \sqrt{d})$

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

Multiply $- 1$ by $- 1$ .

$c - \sqrt{d c} - \sqrt{c d} + 1 \sqrt{d} \sqrt{d}$

Multiply $\sqrt{d}$ by $1$ .

$c - \sqrt{d c} - \sqrt{c d} + \sqrt{d} \sqrt{d}$

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

$c - \sqrt{d c} - \sqrt{c d} + {\sqrt{d}}^{1} \sqrt{d}$

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

$c - \sqrt{d c} - \sqrt{c d} + {\sqrt{d}}^{1} {\sqrt{d}}^{1}$

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

$c - \sqrt{d c} - \sqrt{c d} + {\sqrt{d}}^{1 + 1}$

Add $1$ and $1$ .

$c - \sqrt{d c} - \sqrt{c d} + {\sqrt{d}}^{2}$

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

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

$c - \sqrt{d c} - \sqrt{c d} + {(d^{\frac{1}{2}})}^{2}$

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

$c - \sqrt{d c} - \sqrt{c d} + d^{\frac{1}{2} \cdot 2}$

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

$c - \sqrt{d c} - \sqrt{c d} + d^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$c - \sqrt{d c} - \sqrt{c d} + d^{\frac{2}{2}}$

Rewrite the expression.

$c - \sqrt{d c} - \sqrt{c d} + d^{1}$

Simplify.

$c - \sqrt{d c} - \sqrt{c d} + d$

Subtract $\sqrt{c d}$ from $- \sqrt{d c}$ .

Reorder $d$ and $c$ .

$c - \sqrt{c d} - \sqrt{c d} + d$

Subtract $\sqrt{c d}$ from $- \sqrt{c d}$ .

$c - 2 \sqrt{c d} + d$

Step 4

Move $- 2 \sqrt{c d}$ .

$c + d - 2 \sqrt{c d}$

Simplify ( square root of c- square root of d)^2

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