Question

simplify, using the distributive property.

enter the number that belongs in the green box.

(3(2x + 6) = ?x + )

Explanation:

Identify the given expression

We are given the algebraic expression:

$$ 3(2x + 6) $$

We need to simplify this expression using the distributive property.

Apply the distributive property

The distributive property states that for any real numbers \(a\), \(b\), and \(c\):

$$ a(b + c) = ab + ac $$

Applying this to our expression where \(a = 3\), \(b = 2x\), and \(c = 6\):

$$ 3(2x + 6) = 3 \cdot 2x + 3 \cdot 6 $$

Perform the multiplications

Multiply the terms inside the parentheses by the factor outside:

$$ 3 \cdot 2x = 6x $$

$$ 3 \cdot 6 = 18 $$

Combining these terms gives:

$$ 6x + 18 $$

Identify the value for the green box

The equation is written in the form:

$$ 3(2x + 6) = [ ? ]x + [ \quad ] $$

Comparing \(6x + 18\) to this form, the coefficient of \(x\) (which is in the green box containing the question mark) is \(6\).

Answer:

Simplify, using the distributive property.

Enter the number that belongs in the green box.

\(3(2x + 6) =\) <blank>6</blank>\(x + 18\)