Advertisements
Advertisements
Question
Factorise the following:
64m3 – 343n3
Advertisements
Solution
We know that, x3 − y3 = (x − y)(x2 + xy + y2)
It is given that, 64m3 − 343n3 = (4m)3 − (7n)3
= (4m − 7n)[(4m)2 + (4m)(7n) + (7n)2]
= (4m − 7n)(16m2 + 28mn + 49n2)
APPEARS IN
RELATED QUESTIONS
Evaluate the following product without multiplying directly:
103 × 107
If `x + 1/x = sqrt5`, find the value of `x^2 + 1/x^2` and `x^4 + 1/x^4`
Simplify the following products:
`(2x^4 - 4x^2 + 1)(2x^4 - 4x^2 - 1)`
If \[x - \frac{1}{x} = - 1\] find the value of \[x^2 + \frac{1}{x^2}\]
If \[x^4 + \frac{1}{x^4} = 119\] , find the value of \[x^3 - \frac{1}{x^3}\]
Find the following product:
(3x + 2y) (9x2 − 6xy + 4y2)
Find the following product:
(4x − 5y) (16x2 + 20xy + 25y2)
Find the following product:
\[\left( \frac{3}{x} - \frac{5}{y} \right) \left( \frac{9}{x^2} + \frac{25}{y^2} + \frac{15}{xy} \right)\]
If x = 3 and y = − 1, find the values of the following using in identify:
\[\left( \frac{5}{x} + 5x \right)\] \[\left( \frac{25}{x^2} - 25 + 25 x^2 \right)\]
If x + \[\frac{1}{x}\] = then find the value of \[x^2 + \frac{1}{x^2}\].
If a − b = −8 and ab = −12, then a3 − b3 =
If \[x^4 + \frac{1}{x^4} = 194,\] then \[x^3 + \frac{1}{x^3} =\]
Use the direct method to evaluate :
`("z"-2/3)("z"+2/3)`
Evaluate: `(3"x"+1/2)(2"x"+1/3)`
Evaluate: 20.8 × 19.2
If `"a" - 1/"a" = 10`; find `"a"^2 - 1/"a"^2`
If `"r" - (1)/"r" = 4`; find : `"r"^4 + (1)/"r"^4`
Simplify:
(2x + y)(4x2 - 2xy + y2)
If `x/y + y/x = -1 (x, y ≠ 0)`, the value of x3 – y3 is ______.
Factorise the following:
`(2x + 1/3)^2 - (x - 1/2)^2`
