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100

1-27a3

1 -27a = 13 - (3a)3

          =(1-3a)(1+3a+9a2)


100

5a2 -20ab

5a(a-4b)

100

x3 + 2x2 - 5x -10

x2(x+2)-5(x+2)

(x2-5)(x+2)

100

(49x2 - 1/4)

(7x+1/2)(7x-1/2)

200

2a7- 128a

2a7- 128a = 2a((a2)3 - (4)3)

                =2a(a2 -4)(a4 +4a2+16)

               =2a(a+2)(a-2)(a4 +4a2+16)

200

6xy – 4y + 6 – 9x.

6xy – 4y + 6 – 9x.
=3x( 2y - 3) - 2( 2y - 3)

=(2y - 3) (3x - 2)

200

4x2 - 6xy + 12x

4x2- 6xy + 12x = 2x ( 2x -3y + 6)

200

x2- 4x - 21

(x-7)(x+3)

300

2a2 + 2√6 ab +3b2 

(√2a + √3 b)2

300

x3 – 8y3 + 27 + 18xy

(x – 2y + 3)(x2 + 4y2 + 9 + 2xy – 3x + 6y )  

300

Give possible expression for the length and breadth of the rectangle having 35y2 + 13y – 12 as its area.

(5y +4)(7y - 3)

300

27x3 + y3 + 9x2y + 3xy2

27x3 + y3 + 27x2y + 9xy2

= (3x)3 + (y)3 + 3(3x)2y + 3(3x)y2

= (3x + y)3 [ here a = 3x and b= y;a3 + b3 + 3a2b + 3b2a = (a + b)3 ]

400

x(x – 2) (x – 4) + 4x – 8

x(x – 2) (x – 4) + 4x – 8
= x(x – 2) (x – 4) + 4(x – 2)
= (x – 2) [x(x – 4) + 4]
= (x – 2) (x2 – 4x + 4)
= (x – 2) [(x)2 – 2 x x x 2 + (2)2]
= (x – 2) (x – 2)2 = (x – 2)3

400

(a – b + c)2 + (b – c + a)2 + 2(a – b + c) (b – c + a)

(a – b + c)2 + ( b- c +a)2 + 2(a – b + c) (b – c + a)      {∵ a2 + b2 + 2ab = (a + b)2}
= [a – b + c + b- c + a]2
= (2a)2 = 4a2

400

x(2x - y) -y2

=2x2 - xy - y2

=2x2 - 2xy + xy - y2

=2x(x - y) + y(x - y)

=(2x + y)(x - y)

400

(p + q)2 - 20(p + q) - 125

(p + q - 25)(p + q + 25)