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
Evaluate the following using identities:
(2x + y) (2x − y)
Simplify the following
`(7.83 + 7.83 - 1.17 xx 1.17)/6.66`
If `x + 1/x = sqrt5`, find the value of `x^2 + 1/x^2` and `x^4 + 1/x^4`
Write in the expanded form:
`(m + 2n - 5p)^2`
Write in the expanded form: `(x/y + y/z + z/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)
If x = 3 and y = − 1, find the values of the following using in identify:
\[\left( \frac{3}{x} - \frac{x}{3} \right) \left( \frac{x^2}{9} + \frac{9}{x^2} + 1 \right)\]
If a + b = 10 and ab = 16, find the value of a2 − ab + b2 and a2 + ab + b2
The product (x2−1) (x4 + x2 + 1) is equal to
Use identities to evaluate : (502)2
If a - b = 7 and ab = 18; find a + b.
If x + y = `7/2 "and xy" =5/2`; find: x - y and x2 - y2
Use the direct method to evaluate :
(3x2+5y2) (3x2−5y2)
Evaluate: `(4/7"a"+3/4"b")(4/7"a"-3/4"b")`
Evaluate the following without multiplying:
(999)2
Evaluate the following without multiplying:
(1005)2
If a - b = 10 and ab = 11; find a + b.
If a2 - 3a - 1 = 0 and a ≠ 0, find : `"a"^2 - (1)/"a"^2`
Factorise the following:
`(2x + 1/3)^2 - (x - 1/2)^2`
