Simplify (-7+ square root of 3x)(4+ square root of 3x)

$(- 7 + \sqrt{3 x}) (4 + \sqrt{3 x})$

Step 1

Expand $(- 7 + \sqrt{3 x}) (4 + \sqrt{3 x})$ using the FOIL Method.

Apply the distributive property.

$- 7 (4 + \sqrt{3 x}) + \sqrt{3 x} (4 + \sqrt{3 x})$

Apply the distributive property.

$- 7 \cdot 4 - 7 \sqrt{3 x} + \sqrt{3 x} (4 + \sqrt{3 x})$

Apply the distributive property.

$- 7 \cdot 4 - 7 \sqrt{3 x} + \sqrt{3 x} \cdot 4 + \sqrt{3 x} \sqrt{3 x}$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $- 7$ by $4$ .

$- 28 - 7 \sqrt{3 x} + \sqrt{3 x} \cdot 4 + \sqrt{3 x} \sqrt{3 x}$

Move $4$ to the left of $\sqrt{3 x}$ .

$- 28 - 7 \sqrt{3 x} + 4 \cdot \sqrt{3 x} + \sqrt{3 x} \sqrt{3 x}$

Multiply $\sqrt{3 x} \sqrt{3 x}$ .

Raise $\sqrt{3 x}$ to the power of $1$ .

$- 28 - 7 \sqrt{3 x} + 4 \sqrt{3 x} + {\sqrt{3 x}}^{1} \sqrt{3 x}$

Raise $\sqrt{3 x}$ to the power of $1$ .

$- 28 - 7 \sqrt{3 x} + 4 \sqrt{3 x} + {\sqrt{3 x}}^{1} {\sqrt{3 x}}^{1}$

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

$- 28 - 7 \sqrt{3 x} + 4 \sqrt{3 x} + {\sqrt{3 x}}^{1 + 1}$

Add $1$ and $1$ .

$- 28 - 7 \sqrt{3 x} + 4 \sqrt{3 x} + {\sqrt{3 x}}^{2}$

Rewrite ${\sqrt{3 x}}^{2}$ as $3 x$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3 x}$ as ${(3 x)}^{\frac{1}{2}}$ .

$- 28 - 7 \sqrt{3 x} + 4 \sqrt{3 x} + {({(3 x)}^{\frac{1}{2}})}^{2}$

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

$- 28 - 7 \sqrt{3 x} + 4 \sqrt{3 x} + {(3 x)}^{\frac{1}{2} \cdot 2}$

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

$- 28 - 7 \sqrt{3 x} + 4 \sqrt{3 x} + {(3 x)}^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$- 28 - 7 \sqrt{3 x} + 4 \sqrt{3 x} + {(3 x)}^{\frac{2}{2}}$

Rewrite the expression.

$- 28 - 7 \sqrt{3 x} + 4 \sqrt{3 x} + {(3 x)}^{1}$

Simplify.

$- 28 - 7 \sqrt{3 x} + 4 \sqrt{3 x} + 3 x$

Add $- 7 \sqrt{3 x}$ and $4 \sqrt{3 x}$ .

$- 28 - 3 \sqrt{3 x} + 3 x$

Step 3

Move $- 3 \sqrt{3 x}$ .

$- 28 + 3 x - 3 \sqrt{3 x}$

Step 4

Reorder $- 28$ and $3 x$ .

$3 x - 28 - 3 \sqrt{3 x}$

Simplify (-7+ square root of 3x)(4+ square root of 3x)

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