Advertisements
Advertisements
Question
Write in the expanded form: (ab + bc + ca)2
Advertisements
Solution
We have
(ab + bc + ca)2 = (ab)2 + (bc)2 + (ca )2 + 2 (ab)(bc) + 2(bc)ca + 2 (ab)(ca )
[∵ (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca]
= a2b2 + b2c2 + c2a2 + 2ab2c + 2bc2a + 2a2bc
∴ (ab + bc + ca)2 = a2b2 + b2c2 + c2a2 + 2ab2c + 2bc2a + 2a2bc
APPEARS IN
RELATED QUESTIONS
Evaluate the following product without multiplying directly:
95 × 96
Evaluate the following using identities:
(1.5x2 − 0.3y2) (1.5x2 + 0.3y2)
If 2x + 3y = 8 and xy = 2 find the value of `4x^2 + 9y^2`
If 3x - 7y = 10 and xy = -1, find the value of `9x^2 + 49y^2`
Simplify: `(a + b + c)^2 - (a - b + c)^2`
Find the value of 4x2 + y2 + 25z2 + 4xy − 10yz − 20zx when x = 4, y = 3 and z = 2.
Simplify the following expressions:
`(x^2 - x + 1)^2 - (x^2 + x + 1)^2`
Find the cube of the following binomials expression :
\[\frac{3}{x} - \frac{2}{x^2}\]
If x = 3 and y = − 1, find the values of the following using in identify:
\[\left( \frac{5}{x} + 5x \right)\] \[\left( \frac{25}{x^2} - 25 + 25 x^2 \right)\]
If a + b = 10 and ab = 16, find the value of a2 − ab + b2 and a2 + ab + b2
If a1/3 + b1/3 + c1/3 = 0, then
Evaluate `(a/[2b] + [2b]/a )^2 - ( a/[2b] - [2b]/a)^2 - 4`.
The number x is 2 more than the number y. If the sum of the squares of x and y is 34, then find the product of x and y.
Use the direct method to evaluate :
(2a+3) (2a−3)
Use the direct method to evaluate :
(xy+4) (xy−4)
Evaluate: (6 − 5xy) (6 + 5xy)
Evaluate: 20.8 × 19.2
If x + y = 1 and xy = -12; find:
x2 - y2.
If x + y + z = 12 and xy + yz + zx = 27; find x2 + y2 + z2.
Give possible expressions for the length and breadth of the rectangle whose area is given by 4a2 + 4a – 3.
