Question

Find the product of (x − 3)2.
x2 + 6x + 9
x2 − 9
x2 − 6x + 9
x2 + 9

Answer 1

`\large\boxed{x^2-6x+9}`

Explanation:

`(x-3)^2\\\\\bold{METHOD\ 1}\\\\(x-3)^2=(x-3)(x-3)\qquad\text{use FOIL}\ (a+b)(c+d)=ac+ad+bc+bd\\\\=(x)(x)+(x)(-3)+(-3)(x)+(-3)(-3)\\\\=x^2-3x-3x+9\qquad\text{combine like terms}\\\\=x^2-6x+9\\\\\bold{METHOD\ 2}\\\\(x-3)^2\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\=x^2-2(x)(3)+3^2\\\\=x^2-6x+9`

Answer 2

(x-3)² ⇒ (x-3)(x-3)

(x-3)(x-3) = x(x-3) -3(x-3) ⇒ x² - 3x - 3x + 9 ⇒ x² - 6x + 9

The 3rd option is the correct answer. x² - 6x + 9