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
Expand the following, using suitable identity:
(3a – 7b – c)2
Factorise:
`2x^2 + y^2 + 8z^2 - 2sqrt2xy + 4sqrt2yz - 8xz`
Factorise the following:
8a3 – b3 – 12a2b + 6ab2
Verify:
x3 + y3 = (x + y) (x2 – xy + y2)
What are the possible expressions for the dimensions of the cuboids whose volume is given below?
| Volume : 12ky2 + 8ky – 20k |
Evaluate the following using identities:
(1.5x2 − 0.3y2) (1.5x2 + 0.3y2)
Simplify the following:
0.76 x 0.76 - 2 x 0.76 x 0.24 x 0.24 + 0.24
Find the following product:
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 find the value of \[x^6 + \frac{1}{x^6}\].
If \[3x + \frac{2}{x} = 7\] , then \[\left( 9 x^2 - \frac{4}{x^2} \right) =\]
If 3x + 4y = 16 and xy = 4, find the value of 9x2 + 16y2.
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)
Evaluate the following without multiplying:
(999)2
Simplify:
`("a" - 1/"a")^2 + ("a" + 1/"a")^2`
If a + b + c = 0, then a3 + b3 + c3 is equal to ______.
Factorise the following:
25x2 + 16y2 + 4z2 – 40xy + 16yz – 20xz
Find the value of x3 + y3 – 12xy + 64, when x + y = – 4
