Question

1. write an expression that is equivalent to ((x + 5)^2 - (x + 4)(x + 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 \((x+5)^2=x^{2}+10x + 25\).

Step2: Expand \((x + 4)(x + 1)\)

Using the distributive property \((a + b)(c + d)=ac+ad+bc+bd\), we have \((x + 4)(x + 1)=x^{2}+x+4x + 4=x^{2}+5x + 4\).

Step3: Subtract the two expanded expressions

\((x^{2}+10x + 25)-(x^{2}+5x + 4)=x^{2}+10x + 25 - x^{2}-5x - 4\).

Step4: Combine like terms

Combine the \(x^{2}\) terms: \(x^{2}-x^{2}=0\). Combine the \(x\) terms: \(10x-5x = 5x\). Combine the constant terms: \(25 - 4=21\). So the result is \(5x + 21\).

Answer:

\(5x + 21\)