Question

1. write a simplified expression that is equivalent to \\((2x + 5)(x^2 + 4x - 6)\\)

Explanation:

Step1: Apply distributive property (FOIL for polynomials)

Multiply \(2x\) by each term in \((x^2 + 4x - 6)\) and \(5\) by each term in \((x^2 + 4x - 6)\):
\(2x(x^2 + 4x - 6) + 5(x^2 + 4x - 6)\)
\(= 2x \cdot x^2 + 2x \cdot 4x - 2x \cdot 6 + 5 \cdot x^2 + 5 \cdot 4x - 5 \cdot 6\)

Step2: Simplify each term

Calculate the products:
\(= 2x^3 + 8x^2 - 12x + 5x^2 + 20x - 30\)

Step3: Combine like terms

Combine the \(x^2\) terms and the \(x\) terms:
\(2x^3 + (8x^2 + 5x^2) + (-12x + 20x) - 30\)
\(= 2x^3 + 13x^2 + 8x - 30\)

Answer:

\(2x^3 + 13x^2 + 8x - 30\)