Question

question
expand the expression to a polynomial in standard form:
\\((2x - 1)(3x^2 + 4x - 10)\\)

Explanation:

Step1: Apply the distributive property (FOIL for polynomials)

Multiply \(2x\) by each term in \(3x^{2}+4x - 10\) and \(-1\) by each term in \(3x^{2}+4x - 10\).
\(2x\times(3x^{2}+4x - 10)=2x\times3x^{2}+2x\times4x-2x\times10 = 6x^{3}+8x^{2}-20x\)
\(-1\times(3x^{2}+4x - 10)=-3x^{2}-4x + 10\)

Step2: Combine like terms

Add the two results together:
\((6x^{3}+8x^{2}-20x)+(-3x^{2}-4x + 10)=6x^{3}+(8x^{2}-3x^{2})+(-20x-4x)+10\)
\(=6x^{3}+5x^{2}-24x + 10\)

Answer:

\(6x^{3}+5x^{2}-24x + 10\)