Answer:
[tex]x^{4}[/tex] - 10x³ + 37x² - 60x + 36
Step-by-step explanation:
Given
(x - 3)²(x - 2)² ← expand each factor using FOIL
(x - 3)² = x² - 6x + 9
(x - 2)² = x² - 4x + 4
We now have the product
(x² - 6x + 9)(x² - 4x + 4)
Each term in the second factor is multiplied by each term in the first factor, that is
x²(x² - 4x + 4) - 6x(x² - 4x + 4) + 9(x² - 4x + 4) ← distribute each parenthesis
= [tex]x^{4}[/tex] - 4x³ + 4x² - 6x³ + 24x² - 24x + 9x² - 36x + 36
Collect like terms
= [tex]x^{4}[/tex] - 10x³ + 37x² - 60x + 36
