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The function $h$ is defined as $h(x) = 2x^{2} + 6$ . $\newline$ Find $h(x+4)$ . $\newline$ Write your answer without parentheses, and simplify it as much as possible. $\newline$ $h(x+4) =$ $\square$

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Complex conjugate theorem

Full solution

Q. The function

h

is defined as

h(x) = 2x^{2} + 6

.

\newline

Find

h(x+4)

.

\newline

Write your answer without parentheses, and simplify it as much as possible.

\newline

h(x+4) =

\square

Substitute $x+4$ into $h$ : To find $h(x+4)$ , we need to substitute $(x+4)$ into the function $h$ in place of $x$ . $\newline$ $h(x) = 2x^2 + 6$ , so $h(x+4)$ will be calculated by replacing $x$ with $(x+4)$ in the function.
Expand $(x+4)^2$ : Substitute $(x+4)$ into the function $h$ . $\newline$ $h(x+4) = 2(x+4)^2 + 6$ $\newline$ Now we need to expand $(x+4)^2$ .
Distribute $2$ across terms: Expand $(x+4)^2$ using the formula $(a+b)^2 = a^2 + 2ab + b^2$ . $(x+4)^2 = x^2 + 2\times x\times 4 + 4^2$ $= x^2 + 8x + 16$
Combine constant terms: Substitute the expanded form of $(x+4)^2$ back into the function $h$ . $h(x+4) = 2(x^2 + 8x + 16) + 6$ Now we need to distribute the $2$ across the terms inside the parentheses.
Combine constant terms: Substitute the expanded form of $(x+4)^2$ back into the function $h$ .
$h(x+4) = 2(x^2 + 8x + 16) + 6$
Now we need to distribute the $2$ across the terms inside the parentheses.Distribute the $2$ to each term inside the parentheses.
$h(x+4) = 2\cdot x^2 + 2\cdot 8x + 2\cdot 16 + 6$
$= 2x^2 + 16x + 32 + 6$
Now we need to combine like terms.
Combine constant terms: Substitute the expanded form of $(x+4)^2$ back into the function $h$ .
$h(x+4) = 2(x^2 + 8x + 16) + 6$
Now we need to distribute the $2$ across the terms inside the parentheses.Distribute the $2$ to each term inside the parentheses.
$h(x+4) = 2\cdot x^2 + 2\cdot 8x + 2\cdot 16 + 6$
$= 2x^2 + 16x + 32 + 6$
Now we need to combine like terms.Combine the constant terms $32$ and $6$ .
$h(x+4) = 2x^2 + 16x + 38$
This is the simplified form of $h$ $0$ without parentheses.

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