Question Find the values of $x^{2}+1$ , $(x+1)^{2}$ , and $x^{2}+2x+1$ when $x=4$ .

Studdy Solution

STEP 1

Assumptions1. The value of $x$ is given as4. We are asked to find the value of three expressions $x^{}+1$ , $(x+1)^{}$ , and $x^{}+x+1$

STEP 2

First, let's find the value of the expression $x^{2}+1$ by substituting $x=4$ into the expression.
$x^{2}+1 =4^{2}+1$

STEP 3

Calculate the value of the expression $x^{2}+1$ .
$x^{2}+1 =^{2}+1 =16+1 =17$

STEP 4

Next, let's find the value of the expression $(x+1)^{2}$ by substituting $x=4$ into the expression.
$(x+1)^{2} = (4+1)^{2}$

STEP 5

Calculate the value of the expression $(x+1)^{2}$ .
$(x+1)^{2} = (4+1)^{2} =5^{2} =25$

STEP 6

Finally, let's find the value of the expression $x^{2}+2x+1$ by substituting $x=4$ into the expression.
$x^{2}+2x+1 =4^{2}+2*4+1$

STEP 7

Calculate the value of the expression $x^{2}+2x+1$ .
$x^{2}+2x+1 =4^{2}+2*4+1 =16++1 =25$ So, when $x=4$ , the values of the expressions are $17$ , $25$ , and $25$ respectively.

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