Question

question 10
convert the expression ((x - 3)^2 - 4) into standard and factored form.
standard form:
factored form:

Explanation:

Step1: Expand the squared term

$(x-3)^2 = x^2 - 6x + 9$

Step2: Subtract 4 to get standard form

$x^2 - 6x + 9 - 4 = x^2 - 6x + 5$

Step3: Recognize difference of squares

$(x-3)^2 - 4 = (x-3)^2 - 2^2$

Step4: Apply difference of squares formula

$(a^2 - b^2) = (a-b)(a+b)$, so $(x-3-2)(x-3+2) = (x-5)(x-1)$

Answer:

standard form: $x^2 - 6x + 5$
factored form: $(x-5)(x-1)$