Advertisements
Advertisements
प्रश्न
Factorize 4( x - y)2 -12( x - y)( x + y ) + 9(x + y )2
उत्तर
Let ( x - y ) = a, ( x + y ) = b
= 4a2 -12ab + 9b2
Splitting middle term -12 = -6 - 6 also 4 x 9 = -6 x -6
= 4a2 - 6ab - 6ab + 9b2
= 2a (2a - 3b) - 3b (2a - 3b)
= (2a - 3b)(2a - 3b)
= (2a - 3b)2
Substituting a = x - y and b = x + y
=[2 ( x - y ) - 3( x + y )]
= [2x - 2 y - 3x - 3y]2
= [2x - 3x - 2 y - 3y]2
= [-x - 5 y]2
= [(-1)(x + 5y)]2 [∵ (-1)2 = 1]
∴ 4( x - y)2 -12( x - y)( x + y) + 9( x + y )2 = (x + 5y)2
APPEARS IN
संबंधित प्रश्न
Factorize the following expressions:
a12 + b12
Simplify `(155 xx 155 xx 155 - 55 xx 55 xx 55)/(155 xx 155 + 155 xx 55 + 55 xx 55)`
Multiply: x2 + 4y2 + 2xy − 3x + 6y + 9 by x − 2y + 3
The expression (a − b)3 + (b − c)3 + (c −a)3 can be factorized as
If 3x = a + b + c, then the value of (x − a)3 + (x −b)3 + (x − c)3 − 3(x − a) (x − b) (x −c) is
Evaluate: (a2 + 2ab + b2)(a + b)
Evaluate: (4m - 2)(m2 + 5m - 6)
Divide: 8x + 24 by 4
Divide: x3 − 6x2 + 11x − 6 by x2 − 4x + 3
Solve the following equation.
3y + 4 = 5y − 6
