Introduction of monomial functions

Introduction of monomial functions :

A term is a variable or a number (which is constant) or a variable with a number attached (called a co-efficient). A single tem is called a monomial. Monomial can be written as f(x) = C (or) f(x) = C. x ⁿ

Where n is a positive integer

k is a constant

How to Solve Monomial Functions:

• To add monomial

You can only add monomial that has the same base. If the bases are same, then we can add their co-efficient.

• To subtract monomial

Like in addition, for subtraction also the monomial should be of same bases. The co-efficient is subtracted then.

• To multiply monomial

If there are coefficients on the terms then we must first multiply coefficients by coefficients. Then we can multiply the variable of one term by the other.

• To divide monomial

When we divide the monomial, remember that the numerical coefficients are divided and then the literal coefficients (such as a and b).

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Sample Problems for Monomial Functions:

Pro 1:  Add the following monomial 5x, 2y, 3x

Sol :    Here we have two different terms x and y. We can add only the coefficients of same monomial.

            = (5x + 3x) + 2y

            = 8x + 2y

Pro 2 :  Add the monomial 3x³+ 2y³, 3xy, 2xy, 3y³

Sol :     3x³ + 2y³ + 3xy + 2xy + 3y³

            3x³ + 2y³ + 3xy + 2xy + 3y³

            3x³ + 5y³ + 5xy

Pro 3:   Subtract the following: 2x from 5x

Sol :    The bases are same. Hence we can subtract

            = 5x – 2x

            = 3x

Pro 4:   Solve monomial 3x³ + 2y³- 3xy-2xy- 3y³

Sol :      = 3x³ + 2y³ - 3xy - 2xy - 3y³

             = 3x³ – 5xy - y³

Pro 5 :  Multiply the following monomial: (3x)(4y)

Sol :    First multiply the coefficients

    (3)(4) = 12

   Then multiply the variables

   (x)(y) = xy

  So the answer is: 12xy

Pro 6 :  Multiply the following monomial: (8x³)(2x⁵)

Sol :    First multiply the coefficients

      (8)(2) = 16

    Multiplying the variables

      (x³)(x⁵) = (x³⁺⁵) = x⁸

   So the answer is 16x

Pro 7 :   Divide 4ax by 2ay

Sol :    First: 4 / 2 = 2

  Second: ax / ay = x/y

   The solution is 2x/y

Pro 8 :  Divide (2a² bc) by  (4ac)

Sol  :    First: 2/4 = 1/2

      Second: a² bc / ac = ab

     The solution is (1/2) ab = ab / 2