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How to Expand and Simplify Polynomials?

TopPolynomial can be defined as any types of expression that can be written using constant, variable and exponent values in it. 2ab2 + 9xy2 - 3x - 20 is an example for polynomial. Now, we will understand the process of how to expand and simplify polynomials.

Steps that are to be followed to expand polynomial are shown below:

Step 1: To solve or expand polynomial, first we take a polynomial expression. Let us consider a polynomial expression (9a + 6) (ac - 5p + ab).

Step 2: Now, we have to multiply both polynomial with each other. We need to multiply each term in one polynomial by each term in the other polynomial. So, we can write the polynomial expression as (9a + 6) (ac - 5p + ab).
If we multiply ‘9a’ by all values of 2nd polynomials and multiply 6 by all values of 2nd polynomial, we get
= (9a2c - 45ap + 9a2b + 6ac -30p + 6ab).

Step 3: Now, combine like terms if present in the above expression. On combining the like term, we get:
= 9a2c + 9a2b - 45ap + 6ab + 6ac - 30p,

Step 4: If the same term is not present in the expression, then it is the required solution. So, after solving, we get (9a2c + 9a2b - 45ap + 6ab + 6ac - 30p).


Using these above steps we can easily solve any polynomial expression. Now, we will see some properties based on polynomial.

Properties of Polynomials:
  • Polynomial expressions are joined using the mathematical operator such as (+, -, *).
  • Polynomial expression cannot be join with division operator.
  • Polynomial expression can also contain negative and fraction values.
  • We can also solve the polynomial expression by using the formula $x = -b \pm $$\frac{\sqrt{b^2 - 4ac}}{2a}$