Advertisements
Advertisements
प्रश्न
Simplify: `(a + b + c)^2 - (a - b + c)^2`
Advertisements
उत्तर
We have
`(a + b + c)^2 - (a - b + c)^2`
`=[(a + b + c)^2] - [a - b + c]^2`
`= a^2 + b^2 + c^2 + 2ab + 2bc + 2ca - [a^2 + b^2 + c^2 - 2ab - 2bc + 2ca]`
`= a^2 + b^2 + c^2 + 2ab + 2bc + 2ca - a^2 - b^2 - c^2 + 2ab + 2bc - 2ca`
`= 4ab + 4bc`
`∴ (a + b + c)^2 - (a - b + c)^2 = 4ab + 4bc`
APPEARS IN
संबंधित प्रश्न
Write the following cube in expanded form:
`[3/2x+1]^3`
Factorise the following:
8a3 + b3 + 12a2b + 6ab2
Verify that `x^3+y^3+z^3-3xyz=1/2(x+y+z)[(x-y)^2+(y-z)^2+(z-x)^2]`
Evaluate following using identities:
(a - 0.1) (a + 0.1)
Write in the expanded form: `(x + 2y + 4z)^2`
Evaluate of the following:
(9.9)3
If `x - 1/x = 3 + 2sqrt2`, find the value of `x^3 - 1/x^3`
Find the following product:
\[\left( 3 + \frac{5}{x} \right) \left( 9 - \frac{15}{x} + \frac{25}{x^2} \right)\]
Find the following product:
If x = 3 and y = − 1, find the values of the following using in identify:
\[\left( \frac{x}{7} + \frac{y}{3} \right) \left( \frac{x^2}{49} + \frac{y^2}{9} - \frac{xy}{21} \right)\]
If \[\frac{a}{b} + \frac{b}{a} = 1\] then a3 + b3 =
Use identities to evaluate : (502)2
Expand the following:
(3x + 4) (2x - 1)
Expand the following:
(2x - 5) (2x + 5) (2x- 3)
Simplify by using formula :
(x + y - 3) (x + y + 3)
If x + y = 9, xy = 20
find: x2 - y2.
If a2 - 3a - 1 = 0 and a ≠ 0, find : `"a" + (1)/"a"`
Simplify:
(x + y - z)2 + (x - y + z)2
Using suitable identity, evaluate the following:
101 × 102
Expand the following:
(4a – b + 2c)2
