Marissa was asked to create an equivalent form of the rational expression 27h8−18h5+12h3h . Which of the following is a correct equivalent form?(1 point)Responses9h7−6h4+49 h superscript 7 baseline minus 6 h superscript 4 baseline plus 49h8−6h5+4h9 h superscript 8 baseline minus 6 h superscript 5 baseline plus 4 h9h7−6h49 h superscript 7 baseline minus 6 h superscript 4 baselineThis rational expression does not have any equivalent forms.

Answer 1

Let's simplify the expression \( 27h^8 - 18h^5 + 12h^3h \).

First, notice that the term \( 12h^3h \) can be rewritten as \( 12h^4 \). This gives us:

\[ 27h^8 - 18h^5 + 12h^4 \]

Now, we want to factor this expression. To do that, we first look for the greatest common factor (GCF) of the terms. The coefficients are 27, -18, and 12, and the GCF of these numbers is 3. Additionally, the variable part has \( h^4 \) as the lowest power of \( h \).

Now we can factor out \( 3h^4 \):

\[ 3h^4(9h^4 - 6h + 4) \]

Thus, the expression \( 27h^8 - 18h^5 + 12h^4 \) can be factored as:

\[ 3h^4(9h^4 - 6h + 4) \]

Among the provided options, we will look for an equivalent form of the original expression, which could be \( 9h^7 - 6h^4 + 4 \) or some variation thereof. However, the simplified version after factoring is \( 3h^4(9h^4 - 6h + 4) \).

Given the forms provided in your question do not seem to match directly; only the expression \( 9h^4 - 6h + 4 \) is a core part of the factored expression.

If none of the given options correspond to this simplified factorization, the answer would be that the rational expression does not have any equivalent forms listed.

The best equivalent expression is:

\[ 3h^4(9h^4 - 6h + 4) \]

If checking the provided choices, none correctly reflect the factorization conducted and simplified, then the answer to select would be:

This rational expression does not have any equivalent forms.