To determine the first and last terms of the expression \((12x^5 + 4x^4 + 9x^3 - 10x^2 + 15) - (24x^5 + 9x^3 - 7x^2 + 8)\), we will first simplify the expression by distributing the negative sign:
\[ (12x^5 + 4x^4 + 9x^3 - 10x^2 + 15) - (24x^5 + 9x^3 - 7x^2 + 8) \] \[ = 12x^5 + 4x^4 + 9x^3 - 10x^2 + 15 - 24x^5 - 9x^3 + 7x^2 - 8 \]
Next, we combine like terms:
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For the \(x^5\) terms: \[ 12x^5 - 24x^5 = -12x^5 \]
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For the \(x^4\) terms: \[ 4x^4 \]
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For the \(x^3\) terms: \[ 9x^3 - 9x^3 = 0 \]
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For the \(x^2\) terms: \[ -10x^2 + 7x^2 = -3x^2 \]
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For the constant terms: \[ 15 - 8 = 7 \]
Now we can write the simplified expression:
\[ -12x^5 + 4x^4 - 3x^2 + 7 \]
The first term (the term with the highest degree) is \(-12x^5\), and the last term (the constant term) is \(7\).
Thus, the first term is: \(-12x^5\)
And the last term is: \(7\)
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