monomial multiplication and division

A monomial is an expression that is formed only by a algebraic term only, for example:

  • P (x) = 4x²
  • j (x, y, z) = 5x3y4z2
  • q (x, y) = x³y²

The expression p (x, y) = x²y + xy, is not a monomial, since it has plus of an algebraic term.

How to multiply and divide a monomial

To effectively achieve the multiplication and division of monomials, we must first take into account the sign, then the coefficients and finally the powers.

Example 1: Multiply the following monomials (5x³y) × (- 3y4z)

Remembering the property of the power na × nb = na + b, we have:

(5x³y) × (- 3y4z) = - 15x3y5z

Example 2: Perform the following division of monomials (8x3y3z4t) ÷ (-2xy2z2)

Remembering the properties of powers na × nb = na + b y 1 / na = n-to, we have:

(8x3y3z4t) ÷ (-2xy2z2) = -4x2and Z2t

Example 3: Multiply the following monomials (3x²y) × (7xy).

Remembering the property of the power na × nb = na + b, we have:

(3x²y) × (7xy) = 21x³y²

Example 4: Carry out the following division of monomials (6x²y³) ÷ (-2xy).

Remembering the properties of powers na × nb = na + b y 1 / na = n-to, we have:

(6x²y³) ÷ (-2xy) = -3xy²