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${:[g(x)=9x-2],[h(x)=3x^(2)+2x]:} Write h(g(x)) as an expression in terms of x. h(g(x))= ◻$

$\begin{array}{l} g(x)=9 x-2 \\ h(x)=3 x^{2}+2 x \end{array}$ $\newline$ Write $h(g(x))$ as an expression in terms of $x$ . $\newline$ $h(g(x))=$ $\newline$ $\square$

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Evaluate an exponential function

Full solution

Q.

\begin{array}{l} g(x)=9 x-2 \\ h(x)=3 x^{2}+2 x \end{array}

\newline

Write

h(g(x))

as an expression in terms of

x

.

\newline

h(g(x))=

\newline

\square

Expand Expression: Now, let's expand $(9x-2)^2$ . $(9x-2)^2 = (9x-2)\cdot(9x-2) = 81x^2 - 18x - 18x + 4$
Simplify Expanded Form: Simplify the expanded form. $\newline$ $81x^2 - 18x - 18x + 4 = 81x^2 - 36x + 4$
Multiply by $3$ : Now, multiply the simplified form by $3$ . $3\times(81x^2 - 36x + 4) = 243x^2 - 108x + 12$
Multiply by $2$ : Next, multiply $2$ by $(9x-2)$ . $\$2\cdot(9x-2) = 18x - 4$
Add Results: Finally, add the two results together to get $h(g(x))$ . $\newline$ $h(g(x)) = (243x^2 - 108x + 12) + (18x - 4)$
Combine Like Terms: Combine like terms. $\newline$ $h(g(x)) = 243x^2 - 108x + 12 + 18x - 4$ $\newline$ $h(g(x)) = 243x^2 - 90x + 8$

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