Finite Math Examples

$(8 \sqrt{x} + 9) (7 \sqrt{x} - 2)$

Step 1

Expand $(8 \sqrt{x} + 9) (7 \sqrt{x} - 2)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$8 \sqrt{x} (7 \sqrt{x} - 2) + 9 (7 \sqrt{x} - 2)$

Step 1.2

Apply the distributive property.

$8 \sqrt{x} (7 \sqrt{x}) + 8 \sqrt{x} \cdot - 2 + 9 (7 \sqrt{x} - 2)$

Step 1.3

Apply the distributive property.

$8 \sqrt{x} (7 \sqrt{x}) + 8 \sqrt{x} \cdot - 2 + 9 (7 \sqrt{x}) + 9 \cdot - 2$

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $8 \sqrt{x} (7 \sqrt{x})$ .

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Step 2.1.1.1

Multiply $7$ by $8$ .

$56 \sqrt{x} \sqrt{x} + 8 \sqrt{x} \cdot - 2 + 9 (7 \sqrt{x}) + 9 \cdot - 2$

Step 2.1.1.2

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

$56 ({\sqrt{x}}^{1} \sqrt{x}) + 8 \sqrt{x} \cdot - 2 + 9 (7 \sqrt{x}) + 9 \cdot - 2$

Step 2.1.1.3

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

$56 ({\sqrt{x}}^{1} {\sqrt{x}}^{1}) + 8 \sqrt{x} \cdot - 2 + 9 (7 \sqrt{x}) + 9 \cdot - 2$

Step 2.1.1.4

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

$56 {\sqrt{x}}^{1 + 1} + 8 \sqrt{x} \cdot - 2 + 9 (7 \sqrt{x}) + 9 \cdot - 2$

Step 2.1.1.5

Add $1$ and $1$ .

$56 {\sqrt{x}}^{2} + 8 \sqrt{x} \cdot - 2 + 9 (7 \sqrt{x}) + 9 \cdot - 2$

Step 2.1.2

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

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Step 2.1.2.1

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

$56 {(x^{\frac{1}{2}})}^{2} + 8 \sqrt{x} \cdot - 2 + 9 (7 \sqrt{x}) + 9 \cdot - 2$

Step 2.1.2.2

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

$56 x^{\frac{1}{2} \cdot 2} + 8 \sqrt{x} \cdot - 2 + 9 (7 \sqrt{x}) + 9 \cdot - 2$

Step 2.1.2.3

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

$56 x^{\frac{2}{2}} + 8 \sqrt{x} \cdot - 2 + 9 (7 \sqrt{x}) + 9 \cdot - 2$

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.

$56 x^{\frac{2}{2}} + 8 \sqrt{x} \cdot - 2 + 9 (7 \sqrt{x}) + 9 \cdot - 2$

Step 2.1.2.4.2

Rewrite the expression.

$56 x^{1} + 8 \sqrt{x} \cdot - 2 + 9 (7 \sqrt{x}) + 9 \cdot - 2$

Step 2.1.2.5

Simplify.

$56 x + 8 \sqrt{x} \cdot - 2 + 9 (7 \sqrt{x}) + 9 \cdot - 2$

Step 2.1.3

Multiply $- 2$ by $8$ .

$56 x - 16 \sqrt{x} + 9 (7 \sqrt{x}) + 9 \cdot - 2$

Step 2.1.4

Multiply $7$ by $9$ .

$56 x - 16 \sqrt{x} + 63 \sqrt{x} + 9 \cdot - 2$

Step 2.1.5

Multiply $9$ by $- 2$ .

$56 x - 16 \sqrt{x} + 63 \sqrt{x} - 18$

Step 2.2

Add $- 16 \sqrt{x}$ and $63 \sqrt{x}$ .

$56 x + 47 \sqrt{x} - 18$