What is the simplified form of the following expression? Assume x0 4 2x 4 24×3 4 24×3 4 16x 4 Mark this and return Save a
The correct answer and explanation is:
It looks like your mathematical expression might have formatting issues. Could you clarify the expression so I can simplify it accurately? It seems like you are referring to a polynomial with terms involving xx.
If you meant: 4×4+24×3+24×3+16x44x^4 + 24x^3 + 24x^3 + 16x^4
We can simplify by combining like terms:
- Combine the x4x^4 terms: 4×4+16×4=20x44x^4 + 16x^4 = 20x^4
- Combine the x3x^3 terms: 24×3+24×3=48x324x^3 + 24x^3 = 48x^3
Thus, the simplified form of the given expression is: 20×4+48x320x^4 + 48x^3
Explanation (300 Words):
Polynomial expressions consist of terms with variables raised to different powers. To simplify a polynomial, we group and combine like terms—terms that have the same variable raised to the same exponent.
In this case, we were given: 4×4+24×3+24×3+16x44x^4 + 24x^3 + 24x^3 + 16x^4
The first step was identifying like terms. The terms with x4x^4 are 4x44x^4 and 16x416x^4, which add up to 20x420x^4. The terms with x3x^3 are 24x324x^3 and another 24x324x^3, summing to 48x348x^3.
After combining, the final expression is: 20×4+48x320x^4 + 48x^3
This simplified form makes calculations easier and is useful in algebraic manipulations such as factoring, solving equations, and calculus applications. Simplification is a fundamental skill in algebra that helps in understanding and working with mathematical models efficiently.
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