Basic Math Examples

$(3 \sqrt{c} + 7 \sqrt{7}) (3 \sqrt{c} - 7 \sqrt{y})$

Step 1

Expand $(3 \sqrt{c} + 7 \sqrt{7}) (3 \sqrt{c} - 7 \sqrt{y})$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$3 \sqrt{c} (3 \sqrt{c} - 7 \sqrt{y}) + 7 \sqrt{7} (3 \sqrt{c} - 7 \sqrt{y})$

Step 1.2

Apply the distributive property.

$3 \sqrt{c} (3 \sqrt{c}) + 3 \sqrt{c} (- 7 \sqrt{y}) + 7 \sqrt{7} (3 \sqrt{c} - 7 \sqrt{y})$

Step 1.3

Apply the distributive property.

$3 \sqrt{c} (3 \sqrt{c}) + 3 \sqrt{c} (- 7 \sqrt{y}) + 7 \sqrt{7} (3 \sqrt{c}) + 7 \sqrt{7} (- 7 \sqrt{y})$

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $3 \sqrt{c} (3 \sqrt{c})$ .

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Step 2.1.1.1

Multiply $3$ by $3$ .

$9 \sqrt{c} \sqrt{c} + 3 \sqrt{c} (- 7 \sqrt{y}) + 7 \sqrt{7} (3 \sqrt{c}) + 7 \sqrt{7} (- 7 \sqrt{y})$

Step 2.1.1.2

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

$9 ({\sqrt{c}}^{1} \sqrt{c}) + 3 \sqrt{c} (- 7 \sqrt{y}) + 7 \sqrt{7} (3 \sqrt{c}) + 7 \sqrt{7} (- 7 \sqrt{y})$

Step 2.1.1.3

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

$9 ({\sqrt{c}}^{1} {\sqrt{c}}^{1}) + 3 \sqrt{c} (- 7 \sqrt{y}) + 7 \sqrt{7} (3 \sqrt{c}) + 7 \sqrt{7} (- 7 \sqrt{y})$

Step 2.1.1.4

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

$9 {\sqrt{c}}^{1 + 1} + 3 \sqrt{c} (- 7 \sqrt{y}) + 7 \sqrt{7} (3 \sqrt{c}) + 7 \sqrt{7} (- 7 \sqrt{y})$

Step 2.1.1.5

Add $1$ and $1$ .

$9 {\sqrt{c}}^{2} + 3 \sqrt{c} (- 7 \sqrt{y}) + 7 \sqrt{7} (3 \sqrt{c}) + 7 \sqrt{7} (- 7 \sqrt{y})$

Step 2.1.2

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

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Step 2.1.2.1

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

$9 {(c^{\frac{1}{2}})}^{2} + 3 \sqrt{c} (- 7 \sqrt{y}) + 7 \sqrt{7} (3 \sqrt{c}) + 7 \sqrt{7} (- 7 \sqrt{y})$

Step 2.1.2.2

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

$9 c^{\frac{1}{2} \cdot 2} + 3 \sqrt{c} (- 7 \sqrt{y}) + 7 \sqrt{7} (3 \sqrt{c}) + 7 \sqrt{7} (- 7 \sqrt{y})$

Step 2.1.2.3

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

$9 c^{\frac{2}{2}} + 3 \sqrt{c} (- 7 \sqrt{y}) + 7 \sqrt{7} (3 \sqrt{c}) + 7 \sqrt{7} (- 7 \sqrt{y})$

Step 2.1.2.4

Cancel the common factor of $2$ .

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Step 2.1.2.4.1

Cancel the common factor.

$9 c^{\frac{2}{2}} + 3 \sqrt{c} (- 7 \sqrt{y}) + 7 \sqrt{7} (3 \sqrt{c}) + 7 \sqrt{7} (- 7 \sqrt{y})$

Step 2.1.2.4.2

Rewrite the expression.

$9 c^{1} + 3 \sqrt{c} (- 7 \sqrt{y}) + 7 \sqrt{7} (3 \sqrt{c}) + 7 \sqrt{7} (- 7 \sqrt{y})$

Step 2.1.2.5

Simplify.

$9 c + 3 \sqrt{c} (- 7 \sqrt{y}) + 7 \sqrt{7} (3 \sqrt{c}) + 7 \sqrt{7} (- 7 \sqrt{y})$

Step 2.1.3

Multiply $3 \sqrt{c} (- 7 \sqrt{y})$ .

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Step 2.1.3.1

Multiply $- 7$ by $3$ .

$9 c - 21 \sqrt{c} \sqrt{y} + 7 \sqrt{7} (3 \sqrt{c}) + 7 \sqrt{7} (- 7 \sqrt{y})$

Step 2.1.3.2

Combine using the product rule for radicals.

$9 c - 21 \sqrt{y c} + 7 \sqrt{7} (3 \sqrt{c}) + 7 \sqrt{7} (- 7 \sqrt{y})$

Step 2.1.4

Multiply $7 \sqrt{7} (3 \sqrt{c})$ .

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Step 2.1.4.1

Multiply $3$ by $7$ .

$9 c - 21 \sqrt{y c} + 21 \sqrt{7} \sqrt{c} + 7 \sqrt{7} (- 7 \sqrt{y})$

Step 2.1.4.2

Combine using the product rule for radicals.

$9 c - 21 \sqrt{y c} + 21 \sqrt{c \cdot 7} + 7 \sqrt{7} (- 7 \sqrt{y})$

Step 2.1.5

Multiply $7 \sqrt{7} (- 7 \sqrt{y})$ .

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Step 2.1.5.1

Multiply $- 7$ by $7$ .

$9 c - 21 \sqrt{y c} + 21 \sqrt{c \cdot 7} - 49 \sqrt{7} \sqrt{y}$

Step 2.1.5.2

Combine using the product rule for radicals.

$9 c - 21 \sqrt{y c} + 21 \sqrt{c \cdot 7} - 49 \sqrt{y \cdot 7}$

Step 2.2

Reorder factors in $9 c - 21 \sqrt{y c} + 21 \sqrt{c \cdot 7} - 49 \sqrt{y \cdot 7}$ .

$9 c - 21 \sqrt{y c} + 21 \sqrt{7 c} - 49 \sqrt{7 y}$