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Sagot :
Sure, let's simplify the given expression step by step:
We start with the given expression:
[tex]\[ \left(x^2 + 6x^4 - 4x^3\right) - \left(7x^4 - 4 + 8x^3\right) \][/tex]
First, distribute the negative sign across the second expression inside the parentheses:
[tex]\[ x^2 + 6x^4 - 4x^3 - 7x^4 + 4 - 8x^3 \][/tex]
Next, combine the like terms. Let's organize the terms by their degree for clarity:
1. The [tex]\(x^4\)[/tex] terms: [tex]\(6x^4 - 7x^4 = -x^4\)[/tex]
2. The [tex]\(x^3\)[/tex] terms: [tex]\(-4x^3 - 8x^3 = -12x^3\)[/tex]
3. The [tex]\(x^2\)[/tex] term: [tex]\(x^2\)[/tex]
4. The constant term: [tex]\(4\)[/tex]
Putting it all together, we obtain:
[tex]\[ -x^4 - 12x^3 + x^2 + 4 \][/tex]
Thus, the simplified expression is:
[tex]\[ -x^4 - 12x^3 + x^2 + 4 \][/tex]
We start with the given expression:
[tex]\[ \left(x^2 + 6x^4 - 4x^3\right) - \left(7x^4 - 4 + 8x^3\right) \][/tex]
First, distribute the negative sign across the second expression inside the parentheses:
[tex]\[ x^2 + 6x^4 - 4x^3 - 7x^4 + 4 - 8x^3 \][/tex]
Next, combine the like terms. Let's organize the terms by their degree for clarity:
1. The [tex]\(x^4\)[/tex] terms: [tex]\(6x^4 - 7x^4 = -x^4\)[/tex]
2. The [tex]\(x^3\)[/tex] terms: [tex]\(-4x^3 - 8x^3 = -12x^3\)[/tex]
3. The [tex]\(x^2\)[/tex] term: [tex]\(x^2\)[/tex]
4. The constant term: [tex]\(4\)[/tex]
Putting it all together, we obtain:
[tex]\[ -x^4 - 12x^3 + x^2 + 4 \][/tex]
Thus, the simplified expression is:
[tex]\[ -x^4 - 12x^3 + x^2 + 4 \][/tex]
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