Advertisements
Advertisements
प्रश्न
Find the following product:
Advertisements
उत्तर
Given (1 + x) (1 − x + x2)
We shall use the identity `(a+b)(a^2 - ab +b^2) = a^3 + b^3`
We can rearrange the (1 + x) (1 − x + x2)as
` = (1+x)[(1)^2 - (1)(x)+(x)^2]`
` = (1)^3 + (x)^3`
` = (1)xx (1)xx(1) + (x)xx (x)xx(x)`
` = 1+x^3`
Hence the Product value of `(1+x)(1-x+x^2)`is `1+x^2`
APPEARS IN
संबंधित प्रश्न
Factorise the following:
8a3 – b3 – 12a2b + 6ab2
Verify:
x3 + y3 = (x + y) (x2 – xy + y2)
Simplify: `(a + b + c)^2 - (a - b + c)^2`
Simplify (a + b + c)2 + (a - b + c)2 + (a + b - c)2
Find the cube of the following binomials expression :
\[\frac{1}{x} + \frac{y}{3}\]
Find the cube of the following binomials expression :
\[2x + \frac{3}{x}\]
If \[x + \frac{1}{x} = 5\], find the value of \[x^3 + \frac{1}{x^3}\]
If \[x - \frac{1}{x} = 5\], find the value of \[x^3 - \frac{1}{x^3}\]
If 2x+3y = 13 and xy = 6, find the value of 8x3 + 27y3
Evaluate of the following:
`(10.4)^3`
If `x^4 + 1/x^4 = 194, "find" x^3 + 1/x^3`
If x = 3 and y = − 1, find the values of the following using in identify:
\[\left( \frac{5}{x} + 5x \right)\] \[\left( \frac{25}{x^2} - 25 + 25 x^2 \right)\]
Find the following product:
(4x − 3y + 2z) (16x2 + 9y2 + 4z2 + 12xy + 6yz − 8zx)
If \[x + \frac{1}{x} = 3\] then \[x^6 + \frac{1}{x^6}\] =
If a + b = 7 and ab = 10; find a - b.
Use the direct method to evaluate the following products :
(b – 3) (b – 5)
Use the direct method to evaluate :
(0.5−2a) (0.5+2a)
If `"a" - 1/"a" = 10;` find `"a" + 1/"a"`
Simplify:
(x + y - z)2 + (x - y + z)2
Give possible expressions for the length and breadth of the rectangle whose area is given by 4a2 + 4a – 3.
