Question

which of the following expressions is equivalent to $-3(x^2 - 4y^2)$? choose 1 answer: a $-3x^2 - 12y^2$ b $-3x^2 - 4y^2$ c $-3x^2 + 12y^2$ d $-7x^2y^2$

Explanation:

Step1: Apply the distributive property

The distributive property states that \(a(b - c)=ab - ac\). Here, \(a = - 3\), \(b=x^{2}\) and \(c = 4y^{2}\). So we have \(-3(x^{2}-4y^{2})=-3\times x^{2}-3\times(- 4y^{2})\)

Step2: Simplify the terms

Simplify \(-3\times x^{2}=-3x^{2}\) and \(-3\times(-4y^{2}) = 12y^{2}\) (because multiplying two negative numbers gives a positive number). Combining these terms, we get \(-3x^{2}+12y^{2}\)

Answer:

C. \(-3x^{2}+12y^{2}\)