Advertisements
Advertisements
प्रश्न
Write the following cube in expanded form:
(2a – 3b)3
उत्तर
It is known that,
(a + b)3 = a3 + b3 + 3ab(a + b) and (a − b)3 = a3 − b3 − 3ab(a − b)
(2a − 3b)3 = (2a)3 − (3b)3 – (3 × 2a × 3b)(2a – 3b)
= 8a3 – 27b3 – 18ab(2a – 3b)
= 8a3 – 27b3 – 36a2b + 54ab2
APPEARS IN
संबंधित प्रश्न
Expand the following, using suitable identity:
(2x – y + z)2
Verify that `x^3+y^3+z^3-3xyz=1/2(x+y+z)[(x-y)^2+(y-z)^2+(z-x)^2]`
Without actually calculating the cubes, find the value of the following:
(–12)3 + (7)3 + (5)3
Write in the expanded form:
`(2 + x - 2y)^2`
Write in the expanded form (a2 + b2 + c2 )2
Evaluate of the following:
`(10.4)^3`
Evaluate of the following:
1113 − 893
Find the following product:
(3x + 2y) (9x2 − 6xy + 4y2)
Find the following product:
\[\left( 3 + \frac{5}{x} \right) \left( 9 - \frac{15}{x} + \frac{25}{x^2} \right)\]
Find the following product:
(4x − 3y + 2z) (16x2 + 9y2 + 4z2 + 12xy + 6yz − 8zx)
If a + b + c = 9 and ab + bc + ca = 23, then a2 + b2 + c2 =
If \[\frac{a}{b} + \frac{b}{a} = 1\] then a3 + b3 =
If a2 - 5a - 1 = 0 and a ≠ 0 ; find:
- `a - 1/a`
- `a + 1/a`
- `a^2 - 1/a^2`
Evaluate: `(2"x"-3/5)(2"x"+3/5)`
Evaluate: 20.8 × 19.2
Expand the following:
`(2"a" + 1/(2"a"))^2`
If a2 - 3a - 1 = 0 and a ≠ 0, find : `"a"^2 - (1)/"a"^2`
Multiply x2 + 4y2 + z2 + 2xy + xz – 2yz by (–z + x – 2y).
If a + b + c = 5 and ab + bc + ca = 10, then prove that a3 + b3 + c3 – 3abc = – 25.
