Factor Fourth Degree Expression

In summary, a fourth degree expression is an algebraic expression with one variable raised to the power of four. To simplify it, you can use the rules of exponents. A fourth degree expression differs from a fourth degree polynomial, which only contains terms with a variable raised to the power of four or lower. It can have a negative exponent, which can be simplified using the negative exponent rule. In real-life, it can be used to model various situations and in engineering and physics to calculate complex systems.
  • #1
mathdad
1,283
1
Factor.

x^4 + 2x^2*y^2 + y^4

Must I change x^4 to (x^2)^2 and y^4 to (y^2)^2?

Let u = x^2

Let v = y^2

(u)^2 + 2uv + (v)^2

Where do I go from here?
 
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  • #2
Yes, that's a great start...next, observe that that form is the square of a binomial:

\(\displaystyle (a+b)^2=a^2+2ab+b^2\)
 
  • #3
Great. I can surely finish now.
 

FAQ: Factor Fourth Degree Expression

1. What is a fourth degree expression?

A fourth degree expression is an algebraic expression with one variable raised to the power of four. This means that the highest exponent in the expression is four.

2. How do you simplify a fourth degree expression?

To simplify a fourth degree expression, you can use the rules of exponents to combine like terms and reduce the expression to its simplest form.

3. What is the difference between a fourth degree expression and a fourth degree polynomial?

A fourth degree expression is a general term for any algebraic expression with a variable raised to the power of four. A fourth degree polynomial is a specific type of fourth degree expression that contains only terms with a variable raised to the power of four and lower.

4. Can a fourth degree expression have a negative exponent?

Yes, a fourth degree expression can have a negative exponent. This means that the variable is in the denominator of a fraction. To simplify these expressions, you can use the negative exponent rule to move the variable to the numerator.

5. How is a fourth degree expression used in real-life situations?

A fourth degree expression can be used to model various real-life situations, such as the trajectory of a projectile or the growth of a population. It can also be used in engineering and physics to calculate the behavior of systems with multiple variables and complex relationships.

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