a student factors $3x^{2}-12$ to the following.\n$3(x^{2}-4)$\nwhich statement about $3(x^{2}-4)$ is…

a student factors $3x^{2}-12$ to the following.\n$3(x^{2}-4)$\nwhich statement about $3(x^{2}-4)$ is true?\nthe expression is equivalent, and it is completely factored.\nthe expression is equivalent, but it is not completely factored.\nthe expression is not equivalent, but it is completely factored.\nthe expression is not equivalent, and it is not completely factored.

a student factors $3x^{2}-12$ to the following.\n$3(x^{2}-4)$\nwhich statement about $3(x^{2}-4)$ is true?\nthe expression is equivalent, and it is completely factored.\nthe expression is equivalent, but it is not completely factored.\nthe expression is not equivalent, but it is completely factored.\nthe expression is not equivalent, and it is not completely factored.

Answer

Explanation:

Step1: Check equivalence

Expand (3(x^{2}-4)) using distributive property (a(b + c)=ab+ac). Here (a = 3), (b=x^{2}), (c=-4). (3(x^{2}-4)=3\times x^{2}-3\times4 = 3x^{2}-12). So the expression (3(x^{2}-4)) is equivalent to (3x^{2}-12).

Step2: Check if completely factored

Recall the difference - of - squares formula (a^{2}-b^{2}=(a + b)(a - b)). In the expression (x^{2}-4), we have (a=x) and (b = 2) (since (4=2^{2})). (x^{2}-4=x^{2}-2^{2}=(x + 2)(x - 2)). So (3(x^{2}-4)=3(x + 2)(x - 2)). The original factorization (3(x^{2}-4)) is not completely factored.

Answer:

The expression is equivalent, but it is not completely factored.