Advertisements
Advertisements
Question
Verify:
x3 – y3 = (x – y) (x2 + xy + y2)
Advertisements
Solution
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
RELATED QUESTIONS
Use suitable identity to find the following product:
`(y^2+3/2)(y^2-3/2)`
Factorise:
`2x^2 + y^2 + 8z^2 - 2sqrt2xy + 4sqrt2yz - 8xz`
What are the possible expressions for the dimensions of the cuboids whose volume is given below?
| Volume : 3x2 – 12x |
if `x + 1/x = 11`, find the value of `x^2 + 1/x^2`
Find the cube of the following binomials expression :
\[2x + \frac{3}{x}\]
If 2x+3y = 13 and xy = 6, find the value of 8x3 + 27y3
If 3x − 2y = 11 and xy = 12, find the value of 27x3 − 8y3
Find the value of 27x3 + 8y3, if 3x + 2y = 20 and xy = \[\frac{14}{9}\]
If a + b = 6 and ab = 20, find the value of a3 − b3
If x = −2 and y = 1, by using an identity find the value of the following
Find the following product:
(3x + 2y + 2z) (9x2 + 4y2 + 4z2 − 6xy − 4yz − 6zx)
Find the square of : 3a - 4b
Use the direct method to evaluate the following products:
(x + 8)(x + 3)
Expand the following:
(x - 5) (x - 4)
Simplify by using formula :
(5x - 9) (5x + 9)
If m - n = 0.9 and mn = 0.36, find:
m + n
If a + b + c = 9 and ab + bc + ca = 26, find a2 + b2 + c2.
Without actually calculating the cubes, find the value of:
(0.2)3 – (0.3)3 + (0.1)3
Find the value of x3 – 8y3 – 36xy – 216, when x = 2y + 6
Simplify (2x – 5y)3 – (2x + 5y)3.
