Advertisements
Advertisements
Question
Factorize the following expressions:
a3 + 3a2b + 3ab2 + b3 - 8
Solution
= (a + b)3 - 8 [∵ a3 + 3a2b + 3ab2 + b3 = (a + b)3]
= (a + b)3 - 23
= (a + b - 2)((a + b)2 + (a + b)2 + 22)
= (a + b - 2)(a2 + b2 + 2ab + 2a + 2b + 4)
∴ a3 + 3a2b + 3ab2 + b3 - 8 = (a + b - 2)(a2 + b2 + 2ab + 2a + 2b + 4)
APPEARS IN
RELATED QUESTIONS
Get the algebraic expression in the following case using variables, constants and arithmetic operations.
One-fourth of the product of numbers p and q.
Factorize: `a^2 x^2 + (ax^2 + 1)x + a`
Factorize a2 + 2ab + b2 - c2
Factorize 8a3 + 27b3 + 36a2b + 54ab2
Factorize a3 x3 - 3a2bx2 + 3ab2 x - b3
`2sqrt2a^3 + 3sqrt3b^3 + c^3 - 3 sqrt6abc`
If x2 + y2 = 29 and xy = 2, find the value of x + y.
Write the value of 253 − 753 + 503.
Express the following properties with variables x, y and z.
Commutative property of multiplication
Express the following properties with variables x, y and z.
Distributive property of multiplication over addition
