Question

question
write the following expression as a simplified polynomial in standa
2(x + 5)^2 + 4(x + 5) + 1

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 \((x + 5)^2 = x^2 + 10x + 25\). Then multiply by 2: \(2(x^2 + 10x + 25)=2x^2 + 20x + 50\).

Step2: Expand \(4(x + 5)\)

Using the distributive property \(a(b + c)=ab + ac\), where \(a = 4\), \(b = x\), and \(c = 5\), we get \(4(x + 5)=4x + 20\).

Step3: Combine all terms

Now, add the expanded terms and the constant 1: \((2x^2 + 20x + 50)+(4x + 20)+1\). Combine like terms: \(2x^2+(20x + 4x)+(50 + 20 + 1)=2x^2 + 24x + 71\).

Answer:

\(2x^2 + 24x + 71\)