Question

1. (3x³ - 9x + 7)(x² - 2x + 1)

Explanation:

Step1: Distribute each term

Multiply \(3x^3\) by each term in \((x^2 - 2x + 1)\): \(3x^3 \cdot x^2 = 3x^5\), \(3x^3 \cdot (-2x)= -6x^4\), \(3x^3 \cdot 1 = 3x^3\).
Multiply \(-9x\) by each term: \(-9x \cdot x^2 = -9x^3\), \(-9x \cdot (-2x)= 18x^2\), \(-9x \cdot 1 = -9x\).
Multiply \(7\) by each term: \(7 \cdot x^2 = 7x^2\), \(7 \cdot (-2x)= -14x\), \(7 \cdot 1 = 7\).

Step2: Combine like terms

For \(x^5\): \(3x^5\)
For \(x^4\): \(-6x^4\)
For \(x^3\): \(3x^3 - 9x^3 = -6x^3\)
For \(x^2\): \(18x^2 + 7x^2 = 25x^2\)
For \(x\): \(-9x - 14x = -23x\)
For constants: \(7\)
Combine all terms: \(3x^5 - 6x^4 - 6x^3 + 25x^2 - 23x + 7\)

Answer:

\(3x^5 - 6x^4 - 6x^3 + 25x^2 - 23x + 7\)