Advertisements
Advertisements
Question
Factorize: a (a + b)3 - 3a2b (a + b)
Advertisements
Solution
Taking (a + b) common in two terms
= (a + b){a (a + b)2 - 3a2b}
Now, using (a + b)2 = a2 + b2 + 2ab
= (a + b){a (a2 + b2 + 2ab) - 3a2b}
= (a + b){a3 + ab2 + 2a2b - 3a2b}
= (a + b){a3 + ab2 - a2b}
= (a + b) a{a2 + b2 - ab}
= a (a + b)(a2 + b2 - ab)
∴ a (a + b)3 - 3a2b (a + b) = a (a + b)(a2 + b2 - ab)
APPEARS IN
RELATED QUESTIONS
Factorize `x^2 + 6sqrt2x + 10`
What are the possible expressions for the dimensions of the cuboid whose volume is 3x2 - 12x.
Factorize 8a3 + 27b3 + 36a2b + 54ab2
Find the value of the following expression: 64x2 + 81y2 + 144xy, when x = 11 and \[y = \frac{4}{3}\]
Separate monomials, binomials, trinomials and polynomials from the following algebraic expressions :
8 − 3x, xy2, 3y2 − 5y + 8, 9x − 3x2 + 15x3 − 7,
3x × 5y, 3x ÷ 5y, 2y ÷ 7 + 3x − 7 and 4 − ax2 + bx + y
Evaluate: - 4y (15 + 12y - 8z) (x - 2y)
Divide: 12x3y - 8x2y2 + 4x2y3 by 4xy
Divide: p2 + 4p + 4 by p + 2
Write the coefficient of x2 and x in the following polynomials
`x^2 - 7/2 x + 8`
In a polynomial, the exponents of the variables are always ______.
