# Equivalent expressions of polynomials

### Equivalent expressions of polynomials

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.

#### Lessons

• Introduction
a)
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.

b)
How to find the degree of a polynomial?

• 1.
Identify the coefficient and the number of variables for each expression.
a)
$8x$

b)
$7{x^2}y$

c)
$- ab$

• 2.
Find the like terms.
a)
$3x$       $7y$       $50x$       $x$       $23{x^2}$

b)
$73{a^2}$       $\frac{1}{3}a$       $3{b^2}$       $0.3{c^{}}$       $3{a^2}b$

c)
$15y$       $- 23y$       $13{y^2}z$       $- 10y$       ${x^2}y$

• 3.
Combine like terms.
a)
$x^3 + x^5 + x^3$

b)
${y^2} + {y^5} + 5{y^2} + x + {x^2} + x$

c)
${z^3} - {z^3} + {z^2} + 2{x^5} - 4{y^3} + 3{z^2}$

d)
$x^2 + z^2 + 3x^2 - z^2 - 4x^2$

e)
${z^2} + 3z + 4{z^3} - {3^4} - {z^5}$

f)
$5{y^2} + 4 - 6y + {y^2} - 3 + y$

• 4.
4. Write an equivalent expression with seven terms for each polynomial.
a)
${x^2} + 2x + 3$

b)
$- {y^2} - 3{y^3} - x$

c)
$5x - 3y + 6xy$