Advertisements
Advertisements
प्रश्न
Verify:
x3 – y3 = (x – y) (x2 + xy + y2)
Advertisements
उत्तर
x3 − y3 = (x − y)(x2 + xy + y2)
L.H.S. = x3 − y3
Consider the right-hand side (RHS) and expand it as follows:
R.H.S. = (x − y)(x2 + xy + y2)
R.H.S. = x(x2 + xy + y2) − y(x2 + xy + y2)
R.H.S. = x3 + x2y + xy2 − yx2 − xy2 − y3
R.H.S. = (x3 − y3) + (x2y + xy2 + x2y − xy2)
R.H.S. = x3 − y3
∴ R.H.S. = L.H.S.
Hence, verified.
APPEARS IN
संबंधित प्रश्न
Use suitable identity to find the following product:
(x + 8) (x – 10)
Factorise:
4x2 + 9y2 + 16z2 + 12xy – 24yz – 16xz
Factorise the following:
27 – 125a3 – 135a + 225a2
Evaluate the following using identities:
(0.98)2
Simplify the following products:
`(m + n/7)^3 (m - n/7)`
If \[x^2 + \frac{1}{x^2} = 98\] ,find the value of \[x^3 + \frac{1}{x^3}\]
Simplify of the following:
(x+3)3 + (x−3)3
Find the following product:
\[\left( \frac{3}{x} - \frac{5}{y} \right) \left( \frac{9}{x^2} + \frac{25}{y^2} + \frac{15}{xy} \right)\]
Find the following product:
\[\left( 3 + \frac{5}{x} \right) \left( 9 - \frac{15}{x} + \frac{25}{x^2} \right)\]
If \[x + \frac{1}{x}\] 4, then \[x^4 + \frac{1}{x^4} =\]
If a2 + b2 + c2 − ab − bc − ca =0, then
If a1/3 + b1/3 + c1/3 = 0, then
Use the direct method to evaluate the following products :
(3x – 2y) (2x + y)
Expand the following:
`(2"a" + 1/(2"a"))^2`
Find the squares of the following:
9m - 2n
Simplify by using formula :
(a + b - c) (a - b + c)
Evaluate the following without multiplying:
(95)2
If a2 + b2 + c2 = 41 and a + b + c = 9; find ab + bc + ca.
Using suitable identity, evaluate the following:
9992
