What is the product of the binomials below?

(3x + 6)(4x + 2)

A. [tex]\( 7x^2 + 30x + 8 \)[/tex]
B. [tex]\( 12x^2 + 30x + 12 \)[/tex]
C. [tex]\( 12x^2 + 30x + 8 \)[/tex]
D. [tex]\( 7x^2 + 30x + 12 \)[/tex]



Answer :

To find the product of the binomials [tex]\( (3x + 6)(4x + 2) \)[/tex], we'll follow the standard procedure for multiplying binomials.

1. Identify the terms of the binomials:
[tex]\[ (3x + 6) \quad \text{and} \quad (4x + 2) \][/tex]

2. Multiply each term in the first binomial by each term in the second binomial:
[tex]\[ (3x + 6)(4x + 2) = (3x \cdot 4x) + (3x \cdot 2) + (6 \cdot 4x) + (6 \cdot 2) \][/tex]

3. Compute each product separately:
[tex]\[ 3x \cdot 4x = 12x^2 \][/tex]
[tex]\[ 3x \cdot 2 = 6x \][/tex]
[tex]\[ 6 \cdot 4x = 24x \][/tex]
[tex]\[ 6 \cdot 2 = 12 \][/tex]

4. Combine the resulting terms:
[tex]\[ 12x^2 + 6x + 24x + 12 \][/tex]

5. Simplify by combining like terms (the terms with [tex]\( x \)[/tex] in them):
[tex]\[ 12x^2 + (6x + 24x) + 12 = 12x^2 + 30x + 12 \][/tex]

So, the product of the binomials [tex]\( (3x + 6)(4x + 2) \)[/tex] is [tex]\( 12x^2 + 30x + 12 \)[/tex].

Thus, the correct answer is:
[tex]\[ \boxed{12x^2 + 30x + 12} \][/tex]

Therefore, the answer is option B.