Algebra 1 - Monomials

Introduction

  • An algebraic expression that has a single term is called Monomials.
  • 2, 3xy, 4a2b, and 52m2n3 are some examples of Monomials.
  • In 3xy, the number 3 is called a coefficient.
  • To add or subtract the monomials, perform the operation on the coefficients and keep the variable and exponents the same.
  • The same rules that apply to the addition and subtraction of signed numbers apply to monomials as well.

Adding & Subtracting Monomials

  • To add or subtract the monomials, perform the operation on the coefficients and keep the variable and exponents the same.
  • The same rules that apply to the addition and subtraction of signed numbers apply to monomials as well.

Multiplying and Dividing Monomials

  • To multiply a monomial by a monomial, multiply the numerical coefficient and add the exponents of the same bases.
  • To divide one monomial with another, divide the numerical coefficient and subtract the exponent of the denominator (divisor) from the exponent of the numerator (dividend).
  • The sign number rules apply to monomial multiplications and divisions.
  • Check out the Laws of Exponents rules to learn how to raise a monomial to a power.

Solved Examples

  • 4x + 5x = 9x
  • 3x2 + 5x2 = 7x2
  • 4mn3 + 3mn3 = 7mn3
  • 7x - 3x = 4x
  • 5x2 + 2x2 = 3x2
  • -7a2 + 2a2 + 3a2 = -2a2
  • 4ab + 3ab - 2ab - (-3ab) = 8ab
  • a2a4 = a2+4=a6
  • x3·x5=x3+5=x8
  • 2a2b·3ab4=6a2+1b1+4=6a3b5
  • a5a2=a5-2=a3
  • 12a3b6c2-3ab2c=-4a3-1b6-2c2-1=-4a2b4c

Cheat Sheet

  • Monomials can be added or subtracted only when the terms are alike.
  • The same rules that apply to the addition and subtraction of signed numbers apply to monomials.

Blunder Areas

  • Only monomials with the same variable and exponents (if any) can be added or subtracted.
  • 4ab + 4xy can't be added as the terms/variables are different.