Question

Multiply (x-3)2(x-2)2​

Answer 1

`x^(4)` - 10x³ + 37x² - 60x + 36

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

=
`x^(4)` - 4x³ + 4x² - 6x³ + 24x² - 24x + 9x² - 36x + 36

Collect like terms

=
`x^(4)` - 10x³ + 37x² - 60x + 36