Equivalent expressions of polynomials

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Introduction
Lessons
  2. What is a polynomial?
    • Review on Variables, Coefficients, and Expressions
    • What are Monomials, Binomials, and Trinomials?
    • What are the Degree, Leading Term, and Constant term of a polynomial?
    • Name polynomials based on degree: Quadratic, Cubic, Quartic, Quintic, etc.
  3. How to find the degree of a polynomial?
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Examples
Lessons
  1. Identify the coefficient and the number of variables for each expression.
    1. 8x8x
    2. 7x2y7{x^2}y
    3. −ab - ab
  2. Find the like terms.
    1. 3x3x       7y7y       50x50x       xx       23x223{x^2}
    2. 73a273{a^2}       13a\frac{1}{3}a       3b23{b^2}       0.3c0.3{c^{}}       3a2b3{a^2}b
  3. Combine like terms.
    1. x3+x5+x3x^3 + x^5 + x^3
    2. y2+y5+5y2+x+x2+x{y^2} + {y^5} + 5{y^2} + x + {x^2} + x
    3. z3−z3+z2+2x5−4y3+3z2{z^3} - {z^3} + {z^2} + 2{x^5} - 4{y^3} + 3{z^2}
    4. x2+z2+3x2−z2−4x2x^2 + z^2 + 3x^2 - z^2 - 4x^2
    5. z2+3z+4z3−34−z5{z^2} + 3z + 4{z^3} - {3^4} - {z^5}
    6. 5y2+4−6y+y2−3+y5{y^2} + 4 - 6y + {y^2} - 3 + y
  4. 4. Write an equivalent expression with seven terms for each polynomial.
    1. x2+2x+3{x^2} + 2x + 3
    2. −y2−3y3−x - {y^2} - 3{y^3} - x
    3. 5x−3y+6xy5x - 3y + 6xy
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Topic Notes
A polynomial may contain multiple terms. The variable terms have a coefficient and a variable. Terms with the same variables are called like terms, and they can be combined together. It allows us to write equivalent expressions of polynomials with more or less terms.
Basic Concepts
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