Question

unit 7 review assignment
topic 2: simplifying polynomials

1. ((x - 5)^2 - 3(x + 8))

Explanation:

Step1: Expand \((x - 5)^2\)

Using the formula \((a - b)^2 = a^2 - 2ab + b^2\), where \(a = x\) and \(b = 5\), we get \((x - 5)^2 = x^2 - 10x + 25\).

Step2: Expand \(-3(x + 8)\)

Using the distributive property \(a(b + c) = ab + ac\), we have \(-3(x + 8)=-3x - 24\).

Step3: Combine the expanded expressions

Substitute the expanded forms into the original expression: \((x^2 - 10x + 25)+(-3x - 24)\).

Step4: Combine like terms

Combine the \(x\)-terms and the constant terms: \(x^2+(-10x - 3x)+(25 - 24)=x^2 - 13x + 1\).

Answer:

\(x^2 - 13x + 1\)