# Equivalent expressions of polynomials

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##### Introduction
###### Lessons
1. 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.
2. 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. $8x$
2. $7{x^2}y$
3. $- ab$
2. Find the like terms.
1. $3x$       $7y$       $50x$       $x$       $23{x^2}$
2. $73{a^2}$       $\frac{1}{3}a$       $3{b^2}$       $0.3{c^{}}$       $3{a^2}b$
3. Combine like terms.
1. $x^3 + x^5 + x^3$
2. ${y^2} + {y^5} + 5{y^2} + x + {x^2} + x$
3. ${z^3} - {z^3} + {z^2} + 2{x^5} - 4{y^3} + 3{z^2}$
4. $x^2 + z^2 + 3x^2 - z^2 - 4x^2$
5. ${z^2} + 3z + 4{z^3} - {3^4} - {z^5}$
6. $5{y^2} + 4 - 6y + {y^2} - 3 + y$
4. 4. Write an equivalent expression with seven terms for each polynomial.
1. ${x^2} + 2x + 3$
2. $- {y^2} - 3{y^3} - x$
3. $5x - 3y + 6xy$
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##### Practice
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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.