Question

question
write the following expression as a simplified polynomial in standard form.
2(x - 2)^2 + 4(x - 2) - 6

Explanation:

Step1: Expand \((x - 2)^2\)

Using the formula \((a - b)^2 = a^2 - 2ab + b^2\), where \(a = x\) and \(b = 2\), we have \((x - 2)^2 = x^2 - 4x + 4\). Then multiply by 2: \(2(x - 2)^2 = 2(x^2 - 4x + 4)=2x^2 - 8x + 8\).

Step2: Expand \(4(x - 2)\)

Using the distributive property \(a(b - c)=ab - ac\), we get \(4(x - 2)=4x - 8\).

Step3: Combine all terms

Now substitute the expanded forms back into the original expression: \(2(x - 2)^2 + 4(x - 2)-6=(2x^2 - 8x + 8)+(4x - 8)-6\).
Combine like terms: \(2x^2+(-8x + 4x)+(8 - 8 - 6)=2x^2 - 4x - 6\).

Answer:

\(2x^2 - 4x - 6\)