Question

3x(2x - 3)
which of the following is equivalent to the given expression?
choose 1 answer:
a ( 5x^2 - 9x )
b ( 5x^2 - 6x )
c ( 6x^2 - 9x )
d ( 6x^2 - 3 )

Explanation:

Step1: Apply distributive property

To expand \(3x(2x - 3)\), we use the distributive property \(a(b - c)=ab - ac\). Here, \(a = 3x\), \(b = 2x\), and \(c = 3\). So we multiply \(3x\) with each term inside the parentheses:
\(3x\times2x - 3x\times3\)

Step2: Simplify each term

For the first term, \(3x\times2x=(3\times2)x^{1 + 1}=6x^{2}\) (using the rule \(x^{m}\times x^{n}=x^{m + n}\)). For the second term, \(3x\times3 = 9x\). So the expanded form is \(6x^{2}-9x\).

Answer:

C. \(6x^{2}-9x\)