Factoring Trinomial Squares

Introduction to factoring trinomial squares:

In math, factoring trinomials square method is one significant in basic algebra. It is definite because the operation of sum of three monomials. Given term consists of three expressions that are in the standard form of ax^2 + bx + c. Factoring trinomial is the operation to make arithmetic operation of multiplication in a reverse way. Let us resolve some instance problems for factoring trinomials are x^2 +6x – 5.

Factoring Trinomial Squares:

A trinomial is a polynomial representing of three terms. A trinomial is an equation concerning three expressions. A trinomial is the extension of a power of a computation of three expressions into monomials. The expansion is specified by

`(a+b+c)^(n) = sum_(i,j,k) ((n),(i,j,kk))a^ib^jc^k`     where n is a non negative integer also the computation is in use over all grouping of nonnegative index i, j, and k such to i+j+k = n. The trinomial coefficients are known with  `((n),(i,jk)) = (n!)/(i!j!k!)`

This method is a particular case of the multi nominal method for m = 3. The number of expressions of an extended trinomial is     `((n+2)(n+1))/(2)` Where n is the exponent.

Examples for Factoring Trinomial Squares:

Example 1:

how to solve factoring trinomial square x^2+8x+15

Solution:

Step 1: the given trinomial is x^2+8x+15

Step 2: to factoring this equation is (x+3)(x+5)

so the solution is (x+3)(x+5)

Example 2:

how to solve factoring trinomial square (x+6)2

Solution:

Step 1: the given equation is (x+6)2

Step 2: (a+b)2 = (a2+2ab+b2)

Step 3: using this formula in the given equation

(x+6)2  = (x^2+12x+36)

so the solution is (x^2+12x+36)

Example 3:

how to solve factoring trinomial square (x-2)2

Solution:

Step 1: the given equation is (x-2)2

Step 2: (a-b)2 = (a2-2ab+b2)

Step 3: using this formula in the given equation

(x-2)2  = (x^2-4x+4)

so the solution is (x^2-4x+4)

Example 4:

how to solve factoring trinomial square 9-16x^2

Solution:

Step 1: the given equation is 9-16x^2

Step 2: a2-b2= (a+b)(a-b)

Step 3: using this formula in the given equation is

32-4x^2 = (3+4x) (3-4x)

so the solution of the given equation is   (3+4x) (3-4x)