Question

simplify the following expression.
$(2x^2 - 3x + 6)(x + 9)$
$2x^3 + ?x^2 + \quadx + \quad$

Explanation:

Step1: Distribute \(2x^2\) in \((x + 9)\)

\(2x^2 \times x = 2x^3\), \(2x^2 \times 9 = 18x^2\)

Step2: Distribute \(-3x\) in \((x + 9)\)

\(-3x \times x = -3x^2\), \(-3x \times 9 = -27x\)

Step3: Distribute \(6\) in \((x + 9)\)

\(6 \times x = 6x\), \(6 \times 9 = 54\)

Step4: Combine like terms for \(x^2\)

\(18x^2 - 3x^2 = 15x^2\)

Step5: Combine like terms for \(x\)

\(-27x + 6x = -21x\)

Answer:

The coefficient of \(x^2\) is \(15\), the coefficient of \(x\) is \(-21\), and the constant term is \(54\). So the simplified expression is \(2x^3 + 15x^2 - 21x + 54\).