Question

expand the expression to a polynomial in standard form:
$(3x - 1)(3x^2 - 5x - 2)$

Explanation:

Step1: Apply distributive property (FOIL for polynomials)

Multiply \(3x\) by each term in \(3x^2 - 5x - 2\) and \(-1\) by each term in \(3x^2 - 5x - 2\).
\(3x\times3x^2 = 9x^3\), \(3x\times(-5x)= -15x^2\), \(3x\times(-2)= -6x\)
\(-1\times3x^2 = -3x^2\), \(-1\times(-5x)= 5x\), \(-1\times(-2)= 2\)

Step2: Combine like terms

Combine the \(x^2\) terms: \(-15x^2 - 3x^2 = -18x^2\)
Combine the \(x\) terms: \(-6x + 5x = -x\)
The constant term is \(2\), and the \(x^3\) term is \(9x^3\)

So the expanded polynomial is \(9x^3 - 18x^2 - x + 2\)

Answer:

\(9x^3 - 18x^2 - x + 2\)