Advertisements
Advertisements
Question
Using suitable identity, evaluate the following:
1033
Advertisements
Solution
1033 = (100 + 3)3
= (100)3 + (3)3 + 3 × 10 × 3 × (100 + 3) ...[Using identity, (a + b)3 = a3 + b3 + 3ab(a + b)]
= 1000000 + 27 + 900(103)
= 1000027 + 92700
= 1092727
APPEARS IN
RELATED QUESTIONS
Expand the following, using suitable identity:
(3a – 7b – c)2
Evaluate the following using identities:
117 x 83
Simplify the following: 175 x 175 x 2 x 175 x 25 x 25 x 25
Prove that a2 + b2 + c2 − ab − bc − ca is always non-negative for all values of a, b and c
Write in the expanded form: `(x + 2y + 4z)^2`
Simplify (a + b + c)2 + (a - b + c)2 + (a + b - c)2
Simplify the following expressions:
`(x^2 - x + 1)^2 - (x^2 + x + 1)^2`
Simplify of the following:
If a + b + c = 9 and a2+ b2 + c2 =35, find the value of a3 + b3 + c3 −3abc
If \[x + \frac{1}{x} = 2\], then \[x^3 + \frac{1}{x^3} =\]
75 × 75 + 2 × 75 × 25 + 25 × 25 is equal to
Use the direct method to evaluate :
(2a+3) (2a−3)
Find the squares of the following:
(2a + 3b - 4c)
Simplify by using formula :
(2x + 3y) (2x - 3y)
Evaluate the following without multiplying:
(999)2
If `x + (1)/x = 3`; find `x^2 + (1)/x^2`
If m - n = 0.9 and mn = 0.36, find:
m2 - n2.
If a2 - 3a - 1 = 0 and a ≠ 0, find : `"a"^2 - (1)/"a"^2`
If a2 + b2 + c2 = 41 and a + b + c = 9; find ab + bc + ca.
If `49x^2 - b = (7x + 1/2)(7x - 1/2)`, then the value of b is ______.
