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

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

    b)
    7x2y7{x^2}y

    c)
    ab - ab


  • 2.
    Find the like terms.
    a)
    3x       7y       50x       x       23x223{x^2}

    b)
    73a273{a^2}       13a\frac{1}{3}a       3b23{b^2}       0.3c0.3{c^{}}       3a2b3{a^2}b

    c)
    15y       23y - 23y       13y2z13{y^2}z       - 10y       x2y{x^2}y


  • 3.
    Combine like terms.
    a)
    x3+x5+x3x^3 + x^5 + x^3

    b)
    y2+y5+5y2+x+x2+x{y^2} + {y^5} + 5{y^2} + x + {x^2} + x

    c)
    z3z3+z2+2x54y3+3z2{z^3} - {z^3} + {z^2} + 2{x^5} - 4{y^3} + 3{z^2}

    d)
    x2+z2+3x2z24x2x^2 + z^2 + 3x^2 - z^2 - 4x^2

    e)
    z2+3z+4z334z5{z^2} + 3z + 4{z^3} - {3^4} - {z^5}

    f)
    5y2+46y+y23+y5{y^2} + 4 - 6y + {y^2} - 3 + y


  • 4.
    4. Write an equivalent expression with seven terms for each polynomial.
    a)
    x2+2x+3{x^2} + 2x + 3

    b)
    y23y3x - {y^2} - 3{y^3} - x

    c)
    5x3y+6xy5x - 3y + 6xy


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