Advertisements
Advertisements
प्रश्न
Write the following cube in expanded form:
(2a – 3b)3
Advertisements
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
Use suitable identity to find the following product:
(3x + 4) (3x – 5)
Evaluate the following using suitable identity:
(998)3
Factorise the following:
`27p^3-1/216-9/2p^2+1/4p`
Verify:
x3 + y3 = (x + y) (x2 – xy + y2)
Factorise the following:
64m3 – 343n3
Simplify the following products:
`(2x^4 - 4x^2 + 1)(2x^4 - 4x^2 - 1)`
If a2 + b2 + c2 = 16 and ab + bc + ca = 10, find the value of a + b + c.
If \[x - \frac{1}{x} = 5\], find the value of \[x^3 - \frac{1}{x^3}\]
Evaluate the following:
(98)3
Evaluate of the following:
1043 + 963
Find the following product:
If x = 3 and y = − 1, find the values of the following using in identify:
\[\left( \frac{x}{y} - \frac{y}{3} \right) \frac{x^2}{16} + \frac{xy}{12} + \frac{y^2}{9}\]
If a + b = 7 and ab = 12, find the value of a2 + b2
Use the direct method to evaluate :
`("a"/2-"b"/3)("a"/2+"b"/3)`
If `"a"^2 - 7"a" + 1` = 0 and a = ≠ 0, find :
`"a" + (1)/"a"`
Simplify:
`(x - 1/x)(x^2 + 1 + 1/x^2)`
Expand the following:
(–x + 2y – 3z)2
Without actually calculating the cubes, find the value of:
`(1/2)^3 + (1/3)^3 - (5/6)^3`
Give possible expressions for the length and breadth of the rectangle whose area is given by 4a2 + 4a – 3.
Simplify (2x – 5y)3 – (2x + 5y)3.
