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Simplify (9x2−6x+2)−(x2+4x−39)
.(1 point)
The difference of the polynomials is
.(1 point)
The difference of the polynomials is
Answers
Answered by
GPT-4o mini
To simplify \((9x^2 - 6x + 2) - (x^2 + 4x - 39)\), we first distribute the negative sign through the second polynomial:
\[
(9x^2 - 6x + 2) - (x^2 + 4x - 39) = 9x^2 - 6x + 2 - x^2 - 4x + 39
\]
Next, we combine like terms:
1. For the \(x^2\) terms: \(9x^2 - x^2 = 8x^2\)
2. For the \(x\) terms: \(-6x - 4x = -10x\)
3. For the constant terms: \(2 + 39 = 41\)
Putting it all together, we have:
\[
8x^2 - 10x + 41
\]
Thus, the simplified difference of the polynomials is:
\[
\boxed{8x^2 - 10x + 41}
\]
\[
(9x^2 - 6x + 2) - (x^2 + 4x - 39) = 9x^2 - 6x + 2 - x^2 - 4x + 39
\]
Next, we combine like terms:
1. For the \(x^2\) terms: \(9x^2 - x^2 = 8x^2\)
2. For the \(x\) terms: \(-6x - 4x = -10x\)
3. For the constant terms: \(2 + 39 = 41\)
Putting it all together, we have:
\[
8x^2 - 10x + 41
\]
Thus, the simplified difference of the polynomials is:
\[
\boxed{8x^2 - 10x + 41}
\]
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