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Simplify [tex]\((2x + 3)(x - 4)\)[/tex].

A. [tex]\(2x^2 - 5x - 12\)[/tex]
B. [tex]\(2x^2 + 5x + 12\)[/tex]
C. [tex]\(2x^2 - 5x + 12\)[/tex]
D. [tex]\(2x^2 + 5x - 12\)[/tex]

Sagot :

GinnyAnswer
Sure, let's simplify the expression [tex]\((2x + 3)(x - 4)\)[/tex] step by step.

1. Distribute each term in the first binomial to each term in the second binomial:
[tex]\[ (2x + 3)(x - 4) = 2x \cdot x + 2x \cdot (-4) + 3 \cdot x + 3 \cdot (-4) \][/tex]

2. Multiply the terms:
[tex]\[ 2x \cdot x = 2x^2 \][/tex]
[tex]\[ 2x \cdot (-4) = -8x \][/tex]
[tex]\[ 3 \cdot x = 3x \][/tex]
[tex]\[ 3 \cdot (-4) = -12 \][/tex]

3. Combine all these results together:
[tex]\[ 2x^2 + (-8x) + 3x + (-12) \][/tex]

4. Simplify by combining like terms:
[tex]\[ 2x^2 + (-8x + 3x) - 12 \][/tex]
[tex]\[ = 2x^2 - 5x - 12 \][/tex]

Therefore, the simplified form of [tex]\((2x + 3)(x - 4)\)[/tex] is:
[tex]\[ 2x^2 - 5x - 12 \][/tex]

The correct choice from the given options is:

A. [tex]\(2x^2 - 5x - 12\)[/tex].
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