Mathguru – Help – To find the given square using suitable identity.

9.5 What is an identity? > No. 3(iv)

To find the given square using suitable identity.

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Explanation:

Factorization

In mathematics, factorization (also factorisation in British English) or factoring is the decomposition of an object (for example, a number, a polynomial, or a matrix) into a product of other objects, or factors, which when multiplied together give the original. For example, the number 15 factors into primes as 3 × 5, and the polynomial x² − 4 factors as (x − 2) (x + 2). In all cases, a product of simpler objects is obtained.

Polynomials

Quadratic polynomials

Any quadratic polynomial over the complex numbers (polynomials of the form $ax$ $2$ $+$ $b x$ $+$ $c$ where $a$ , $b$ , and $c$ ∈ $Description: Description: \mathbb{C}$ ) can be factored into an expression with the form $Description: Description: a(x - \alpha)(x - \beta) \$ using the quadratic formula.

$Description: Description: \begin{align} ax^2 + bx + c & = a(x - \alpha)(x - \beta) \\ & = a\left(x - \frac{-b + \sqrt{b^2-4ac}}{2a}\right) \left(x - \frac{-b - \sqrt{b^2-4ac}}{2a}\right), \end{align}$

where $α$ and $β$ are the two roots of the polynomial, found with the quadratic formula.

Perfect square trinomials

A visual illustration of the identity (a + b)² = a² + 2ab + b²

Some quadratics can be factored into two identical binomials. These quadratics are called perfect square trinomials. Perfect square trinomials can be factored as follows:

$Description: Description: a^2 + 2ab + b^2 = (a + b)^2,\,\!$

(Our solved example in mathguru.com uses this concept)

and

$Description: Description: a^2 - 2ab + b^2 = (a - b)^2.\,\!$

http://en.wikipedia.org/wiki/Factorization

The above explanation is copied from Wikipedia, the free encyclopedia and is remixed as allowed under the Creative Commons Attribution- ShareAlike 3.0 Unported License.