Question

expand the expression to a polynomial in standard form: (x - 2)(x - 2)(x - 3)

Explanation:

Step1: Multiply the first two binomials

First, multiply \((x - 2)(x - 2)\). Using the formula \((a - b)^2=a^2 - 2ab + b^2\) where \(a = x\) and \(b = 2\), we get \((x - 2)^2=x^2-4x + 4\).

Step2: Multiply the result by the third binomial

Now, multiply \((x^2-4x + 4)\) by \((x - 3)\). Using the distributive property (also known as the FOIL method for binomials, extended for polynomials):

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Step3: Combine like terms

Combine the like terms \(-3x^2-4x^2=-7x^2\) and \(12x + 4x = 16x\). So the polynomial becomes \(x^3-7x^2+16x-12\).

Answer:

\(x^3 - 7x^2 + 16x - 12\)