Advertisements
Advertisements
Question
x3 - 8y3 + 27z3 +18xyz
Advertisements
Solution
= x3 + (-2 y )3 + (3z )3 - 3 × x × (-2 y )(3z )
= (x + (-2 y ) + 3z )(x2 + (-2y)2 + (3z)2 - x (-2y) - (-2y)(3z) - 3z (x )) [∵ a3 + b3 + c3 - 3abc = (a + b + c)(a2 + b2 + c2 - ab - bc - ca )]
= ( x - 2 y + 3z )(x2 + 4 y2 + 9z2 + 2xy + 6 yz - 3zx)
∴ x3 - 8y3 + 27z3 +18xyz = ( x - 2 y + 3z )(x2 + 4 y2 + 9z2 + 2xy + 6 yz - 3zx)
APPEARS IN
RELATED QUESTIONS
Factorize a2 + 4b2 - 4ab - 4c2
Factorize `5sqrt5x^2 + 20x + 3sqrt5`
Factorize the following expressions
64a3 – b3
Evaluate: (4m - 2)(m2 + 5m - 6)
Multiply: (2x + 3y)(2x - 3y)
Divide: 12x3y - 8x2y2 + 4x2y3 by 4xy
If x = 2 and y = 3, then find the value of the following expressions
x + 1 – y
Rohan’s mother gave him ₹ 3xy2 and his father gave him ₹ 5(xy2 + 2). Out of this total money he spent ₹ (10 – 3xy2) on his birthday party. How much money is left with him?
Express the following properties with variables x, y and z.
Commutative property of multiplication
Which of the following statements about polynomials is correct?
