Question

Select all expressions below that are equivalent to 4x² - 16.

a) 4(4x - 4)
b) 0
c) 4(x - 2)(x + 2)
d) 4(x² – 16)

Answer 1

Option c), 4(x - 2)(x + 2), is the correct choice as it is the factored form of the difference of squares, 4x² - 16. Options a), b), and d) are incorrect as they do not represent equivalent expressions.

Step-by-step explanation:

The student has been asked to select all expressions that are equivalent to the quadratic equation 4x² - 16. This expression can be factored as it is a difference of squares, giving us the equivalent expression, 4(x - 2)(x + 2), which matches option c). Options a) and d) are not equivalent because they do not correctly factor the original expression. Option b) is clearly not equivalent as it simplifies to 0 which is not the same as 4x² - 16.

Looking at the provided examples, they seem to represent various forms of quadratic equations which can be solved using the quadratic formula, but these are not directly relevant to the question asked. Hence, the relevant expressions equivalent to 4x² - 16 are identified by recognizing the difference of squares which simplifies to 4(x - 2)(x + 2).