Question

what is the product?
-9x(5 - 2x)
18x² - 45x
-18x² - 45x
-18x - 45x
18x - 45x

Explanation:

Step1: Apply distributive property

Use the distributive property \(a(b - c)=ab - ac\) to expand \(-9x(5 - 2x)\). Here, \(a=-9x\), \(b = 5\), and \(c=2x\). So we have \(-9x\times5-(-9x)\times2x\).

Step2: Simplify each term

Simplify \(-9x\times5=-45x\) and \(-(-9x)\times2x = 18x^{2}\) (because multiplying two negatives gives a positive, and \(x\times x=x^{2}\)).

Step3: Combine the terms

Combining the simplified terms, we get \(18x^{2}-45x\).

Answer:

\(18x^{2}-45x\) (corresponding to the first option: \(18x^{2}-45x\))