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Simplify the following by combining like terms and then write whether the expression is a
monomial, a binomial or a trinomial.
(a) x4 +3x2 y+3x2 y 2 -3x3 y-3xy3+y4 -3y2 x 2+4yx2 -yx3?
monomial, a binomial or a trinomial.
(a) x4 +3x2 y+3x2 y 2 -3x3 y-3xy3+y4 -3y2 x 2+4yx2 -yx3?
Most Upvoted Answer
Simplify the following by combining like terms and then write whether ...
Step 1: Identify the Expression
The expression to simplify is:
x^4 + 3x^2y + 3x^2y^2 - 3x^3y - 3xy^3 + y^4 - 3y^2x^2 + 4yx^2 - yx^3
Step 2: Combine Like Terms
- Identifying Like Terms:
- x^4: 1 term
- x^3y: -3y + (-1)y = -4x^3y
- x^2y: 3x^2y + 4yx^2 - 3y^2x^2 = 4x^2y - 3x^2y = 0 (cancel out)
- x^2y^2: 3x^2y^2: 1 term
- xy^3: -3xy^3: 1 term
- y^4: 1 term
- Combining the Terms:
- The simplified expression is:
x^4 - 4x^3y + 3x^2y^2 - 3xy^3 + y^4
Step 3: Classify the Expression
- Count the Terms:
- There are 5 distinct terms:
- x^4
- -4x^3y
- 3x^2y^2
- -3xy^3
- y^4
- Classification:
Since there are 5 terms, the expression is classified as a polynomial.
However, since it has more than three terms, it is not a monomial, binomial, or trinomial.
Final Result
The simplified expression is:
x^4 - 4x^3y + 3x^2y^2 - 3xy^3 + y^4
And it is classified as a polynomial with 5 terms.
The expression to simplify is:
x^4 + 3x^2y + 3x^2y^2 - 3x^3y - 3xy^3 + y^4 - 3y^2x^2 + 4yx^2 - yx^3
Step 2: Combine Like Terms
- Identifying Like Terms:
- x^4: 1 term
- x^3y: -3y + (-1)y = -4x^3y
- x^2y: 3x^2y + 4yx^2 - 3y^2x^2 = 4x^2y - 3x^2y = 0 (cancel out)
- x^2y^2: 3x^2y^2: 1 term
- xy^3: -3xy^3: 1 term
- y^4: 1 term
- Combining the Terms:
- The simplified expression is:
x^4 - 4x^3y + 3x^2y^2 - 3xy^3 + y^4
Step 3: Classify the Expression
- Count the Terms:
- There are 5 distinct terms:
- x^4
- -4x^3y
- 3x^2y^2
- -3xy^3
- y^4
- Classification:
Since there are 5 terms, the expression is classified as a polynomial.
However, since it has more than three terms, it is not a monomial, binomial, or trinomial.
Final Result
The simplified expression is:
x^4 - 4x^3y + 3x^2y^2 - 3xy^3 + y^4
And it is classified as a polynomial with 5 terms.
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Simplify the following by combining like terms and then write whether the expression is a monomial, a binomial or a trinomial. (a) x4 +3x2 y+3x2 y 2 -3x3 y-3xy3+y4 -3y2 x 2+4yx2 -yx3?
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