# FACTORING TRINOMIAL WITH ALGEBRAIC IDENTITIES

## About "Factoring Trinomial with Algebraic Identities"

Factoring Trinomial with Algebraic Identities :

Here we are going to see some example problems on factoring trinomial with algebraic identities.

## Factoring Trinomial with Algebraic Identities -Examples

Question 1 :

Factorise the following:

(i)  2x2 + 9a + 10

Solution :

=  2a2 + 9a + 10

Since it is a quadratic equation and coefficient of a2 is 2, we have to multiply constant (10) along with 2.

20  =  5 ⋅ 4 and 5 + 4  =  9

=  2a2 + 5a + 4a + 10

=  a(2a + 5) + 2(2a + 5)

=  (a + 2) (2a + 5)

Hence the factors are (a + 2) and (2a + 5).

(ii)  5x2 - 29xy - 42y2

Solution :

=  5x2 - 29xy - 42y2

The product of 5 and 42 is 210. Now we have to split 210 such that the product be 210 and simplified value must be 29.

-35 ⋅ 6 = -210 and -35 + 6  =  -29

=  5x2 - 35xy + 6xy - 42y2

=  5x(x - 7y) + 6y(x - 7y)

=  (5x + 6y)(x - 7y)

(iii)  9 - 18x + 8x2

Solution :

=  8x2 - 18x + 9

Since it is a quadratic equation and coefficient of x2 is 8, we have to multiply constant (9) along with 8.

72  =  -12 ⋅ (-6) and -12 - 6  =  -18

=  8x- 12x - 6x + 9

=  4x(2x - 3) - 3(2x - 3)

=  (4x - 3) (2x - 3)

Hence the factors are (4x - 3) and (2x - 3).

(iv)  6x2 + 16xy + 8y2

Solution :

=  6x2 + 16xy + 8y2

The product of 6 and 8 is 48. Now we have to split 48 such that the product be 48 and simplified value must be 16.

12 ⋅ 4 = 48 and 12 + 4  =  16

=  6x2 + 12xy + 4xy + 8y2

=  6x(x + 2y) + 4y(x + 2y)

=  (6x + 4y) (x +  2y)

=  2(3x + 2y) (x + 2y)

Hence the factors are 2(3x + 2y) and (x + 2y).

(v)  12x2 + 36x2y + 27y2x2

Solution :

=  12x2 + 36x2y + 27y2x2

=  3x2 (4 + 12y + 9y2)

=  3x2 (9y2 + 12y + 4)

=  3x2 (9y+ 6y + 6y + 4)

=  3x2 [3y(3y + 2) + 2(3y + 2)]

=  3x2 (3y + 2)(3y + 2)

Hence the factors are 3x2 (3y + 2)(3y + 2).

(vi)  (a + b)2 + 9(a + b) + 18

Solution :

=  (a + b)2 + 9(a + b) + 18

Let t = a + b

=  t2 + 9t + 18

=  t2 + 3t + 6t + 18

=  t(t + 3) + 6(t + 3)

=  (t + 3)(t + 6)

By applying the value of t, we get

=  (a + b + 3) (a + b + 6) After having gone through the stuff given above, we hope that the students would have understood, "Factoring Trinomial with Algebraic Identities"

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