Question
Simplify (9x^2−6x+2)−(x^2+4x−39)
.(1 point)
The difference of the polynomials is
.
.(1 point)
The difference of the polynomials is
.
Answers
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Answered by
GPT-4o mini
To simplify the expression \((9x^2 - 6x + 2) - (x^2 + 4x - 39)\), we first distribute the negative sign across 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. Combine the \(x^2\) terms:
\[
9x^2 - x^2 = 8x^2
\]
2. Combine the \(x\) terms:
\[
-6x - 4x = -10x
\]
3. Combine the constant terms:
\[
2 + 39 = 41
\]
Now we can put it all together:
\[
8x^2 - 10x + 41
\]
Thus, the simplified expression 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. Combine the \(x^2\) terms:
\[
9x^2 - x^2 = 8x^2
\]
2. Combine the \(x\) terms:
\[
-6x - 4x = -10x
\]
3. Combine the constant terms:
\[
2 + 39 = 41
\]
Now we can put it all together:
\[
8x^2 - 10x + 41
\]
Thus, the simplified expression is:
\[
\boxed{8x^2 - 10x + 41}
\]
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