Advertisements
Advertisements
प्रश्न
Factorise:
4x2 + 9y2 + 16z2 + 12xy – 24yz – 16xz
Advertisements
उत्तर
It is known that,
(x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2zx
4x2 + 9y2 + 16z2 + 12xy – 24yz – 16xz
= (2x)2 + (3y)2 + (−4z)2 + 2(2x)(3y) + 2(3y)(−4z) + 2(−4z)(2x)
= (2x + 3y – 4z)2
= (2x + 3y – 4z)(2x + 3y – 4z)
APPEARS IN
संबंधित प्रश्न
Expand the following, using suitable identity:
`[1/4a-1/2b+1]^2`
Factorise the following:
8a3 – b3 – 12a2b + 6ab2
If x + y + z = 0, show that x3 + y3 + z3 = 3xyz.
Evaluate the following using identities:
(1.5x2 − 0.3y2) (1.5x2 + 0.3y2)
Evaluate of the following:
(9.9)3
Find the following product:
If x = 3 and y = − 1, find the values of the following using in identify:
\[\left( \frac{3}{x} - \frac{x}{3} \right) \left( \frac{x^2}{9} + \frac{9}{x^2} + 1 \right)\]
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 a + b = 8 and ab = 6, find the value of a3 + b3
If a + b = 7 and ab = 12, find the value of a2 + b2
(a − b)3 + (b − c)3 + (c − a)3 =
Use identities to evaluate : (101)2
If a - b = 4 and a + b = 6; find
(i) a2 + b2
(ii) ab
Find the squares of the following:
9m - 2n
Simplify by using formula :
(x + y - 3) (x + y + 3)
Evaluate, using (a + b)(a - b)= a2 - b2.
999 x 1001
If m - n = 0.9 and mn = 0.36, find:
m + n
If a2 - 3a - 1 = 0 and a ≠ 0, find : `"a" - (1)/"a"`
If a2 + b2 + c2 = 41 and a + b + c = 9; find ab + bc + ca.
Expand the following:
`(4 - 1/(3x))^3`
