Advertisements
Advertisements
Question
Factorise the following:
16x2 + 4y2 + 9z2 – 16xy – 12yz + 24xz
Advertisements
Solution
16x2 + 4y2 + 9z2 – 16xy – 12yz + 24xz
= (4x)2 + (–2y)2 + (3z)2 + 2(4x)(–2y) + 2(–2y)(3z) + 2(4x)(3z) ...[Using identity, (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca]
= (4x – 2y + 3z)2
= (4x – 2y + 3z)(4x – 2y + 3z)
APPEARS IN
RELATED QUESTIONS
Factorise the following using appropriate identity:
`x^2 - y^2/100`
Verify:
x3 + y3 = (x + y) (x2 – xy + y2)
Factorise the following:
27y3 + 125z3
Evaluate the following using identities:
(2x + y) (2x − y)
Simplify the following: 175 x 175 x 2 x 175 x 25 x 25 x 25
Simplify (a + b + c)2 + (a - b + c)2 + (a + b - c)2
Evaluate of the following:
933 − 1073
Find the following product:
If x = −2 and y = 1, by using an identity find the value of the following
Find the following product:
(3x + 2y + 2z) (9x2 + 4y2 + 4z2 − 6xy − 4yz − 6zx)
Use identities to evaluate : (101)2
If a2 - 3a + 1 = 0, and a ≠ 0; find:
- `a + 1/a`
- `a^2 + 1/a^2`
Use the direct method to evaluate the following products:
(a – 8) (a + 2)
Evaluate: (5xy − 7) (7xy + 9)
Expand the following:
(2x - 5) (2x + 5) (2x- 3)
If a - b = 10 and ab = 11; find a + b.
If `x + (1)/x = 3`; find `x^2 + (1)/x^2`
Simplify:
(x + 2y + 3z)(x2 + 4y2 + 9z2 - 2xy - 6yz - 3zx)
Prove that (a + b + c)3 – a3 – b3 – c3 = 3(a + b)(b + c)(c + a).
