Question

can you explain me splitting of middle term​

Answer 1

$\large{\underline{\bf{Splitting ~of ~middle~ term:-}}}$

Understanding splitting of middle term from basic :-

Splitting of middle term is basically used in factorisation of quadratic polynomial. If we talk about it, it describes how to factories a quadratic polynomial.

Quadratic polynomial is in the form of ax²+bx+c in which a,b,c are constant and x is variable. According to splitting middle term, if we factories ax²+bx+c then we need to split bx in the form of x and y such as x+y is equal to bx and xy equal to c.

Let understand this with the help of an example :-

Let suppose that a quadratic polynomial is x² + 6x + 8. Now, as we have discussed above that according to splitting the middle term, we need to split 6x in the form of x and y such as x + y equal to 6x and xy equal to 8.

So 4 and 2 is such two numbers which is 4+2 equal to 6 and 4×2 equal to 8.

Factorisation :

x² + 6x + 8

→ x² + 4x + 2x + 8

[take x as common from x² + 4x and 2 from 2x + 8]

→ x(x+4) + 2(x+4)

→ (x+2)(x+4)

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So, this was the basis concept of splitting the middle term.

Answer 2

A N S W E R :

Some algebraic expressions can be factorised the terms suitably in pairs such that :

(i) the terms in each pairs have a common factor, and

(ii) when this common factor is taken out, the same expression is left in each pairs.

Example We can regroup ac + bd + ad + bc as (ac + ad) + (bc + bd). Then, taking out the common factor in each pairs.

ac + bd + ad + bc = a (c + d) + b(c + d).

So, c + d is a factor common to both parts of the expression. Taking, (c + d) out, ac + bd + ad + bc = (c + d)(a + b).

Another possible way of grouping the terms of given expression in order to carry out factorisaion is as follows.

Note There may be more than one possible way of grouping the terms of an expression.

Example Factorise a² + 3b + 3a + ab

Alternative way

a² + 3b + 3a + ab = (a² + ab) + (3a + 3b) = a(a + b) + 3(a + b) = (a + b)(a + 3)