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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))=

g(x)=9x−2h(x)=3x2+2x \begin{array}{l} g(x)=9 x-2 \\ h(x)=3 x^{2}+2 x \end{array} \newlineWrite h(g(x)) h(g(x)) as an expression in terms of x x .\newlineh(g(x))= h(g(x))=

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Q. g(x)=9x−2h(x)=3x2+2x \begin{array}{l} g(x)=9 x-2 \\ h(x)=3 x^{2}+2 x \end{array} \newlineWrite h(g(x)) h(g(x)) as an expression in terms of x x .\newlineh(g(x))= h(g(x))=
  1. Plug into h(x)h(x): Now let's plug g(x)g(x) into h(x)h(x): h(g(x))=h(9x−2)=3(9x−2)2+2(9x−2)h(g(x)) = h(9x - 2) = 3(9x - 2)^2 + 2(9x - 2).
  2. Square the binomial: Next, we need to square the binomial (9x−2)2(9x - 2)^2. This is (9x−2)(9x−2)(9x - 2)(9x - 2).
  3. Combine like terms: Let's do the multiplication: (9x−2)(9x−2)=81x2−18x−18x+4(9x - 2)(9x - 2) = 81x^2 - 18x - 18x + 4.
  4. Substitute back: Now, combine like terms: 81x2−18x−18x+4=81x2−36x+481x^2 - 18x - 18x + 4 = 81x^2 - 36x + 4.
  5. Distribute coefficients: We'll substitute this back into the h(g(x))h(g(x)) expression: h(g(x))=3(81x2−36x+4)+2(9x−2)h(g(x)) = 3(81x^2 - 36x + 4) + 2(9x - 2).
  6. Do the multiplication: Now, distribute the 33 and the 22: h(g(x))=3×81x2−3×36x+3×4+2×9x−2×2h(g(x)) = 3 \times 81x^2 - 3 \times 36x + 3 \times 4 + 2 \times 9x - 2 \times 2.
  7. Combine like terms: Let's do the multiplication: h(g(x))=243x2−108x+12+18x−4h(g(x)) = 243x^2 - 108x + 12 + 18x - 4.
  8. Simplify expression: Finally, combine like terms: h(g(x))=243x2−108x+18x+12−4h(g(x)) = 243x^2 - 108x + 18x + 12 - 4.
  9. Simplify expression: Finally, combine like terms: h(g(x))=243x2−108x+18x+12−4h(g(x)) = 243x^2 - 108x + 18x + 12 - 4.Simplify the expression: h(g(x))=243x2−90x+8h(g(x)) = 243x^2 - 90x + 8.

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