Advertisements
Advertisements
प्रश्न
Multiply x2 + 4y2 + z2 + 2xy + xz – 2yz by (–z + x – 2y).
Advertisements
उत्तर
According to the question:
(x2 + 4y2 + z2 + 2xy + xz – 2yz) × (–z + x – 2y)
Now, multiply as follows:
= {x + (–2y) + (–z)}{(x)2 + (–2y)2 + (–z2) – (x)(–2y) – (–2y)(–z) – (–z)(x)}
= x3 + (–2y)3 + (–z)3 – 3 × x × (–2y) × (–z)
Use the identity:
(a + b + c)(a2 + b2 + c2 – ab – bc – ca) = a3 + b3 + c3 – 3abc
= x3 – 8y3 – z3 – 6xyz
APPEARS IN
संबंधित प्रश्न
Expand the following, using suitable identity:
(x + 2y + 4z)2
Expand the following, using suitable identity:
(–2x + 3y + 2z)2
Expand the following, using suitable identity:
(–2x + 5y – 3z)2
Write the following cube in expanded form:
`[x-2/3y]^3`
Factorise:
27x3 + y3 + z3 – 9xyz
Verify that `x^3+y^3+z^3-3xyz=1/2(x+y+z)[(x-y)^2+(y-z)^2+(z-x)^2]`
If \[x - \frac{1}{x} = \frac{1}{2}\],then write the value of \[4 x^2 + \frac{4}{x^2}\]
If \[x^3 - \frac{1}{x^3} = 14\],then \[x - \frac{1}{x} =\]
Use identities to evaluate : (998)2
Evalute : `( 7/8x + 4/5y)^2`
Evaluate : (4a +3b)2 - (4a - 3b)2 + 48ab.
Use the direct method to evaluate the following products:
(5a + 16) (3a – 7)
Use the direct method to evaluate :
(xy+4) (xy−4)
Evaluate: `(4/7"a"+3/4"b")(4/7"a"-3/4"b")`
Find the squares of the following:
3p - 4q2
Evaluate, using (a + b)(a - b)= a2 - b2.
15.9 x 16.1
If `"a"^2 - 7"a" + 1` = 0 and a = ≠ 0, find :
`"a"^2 + (1)/"a"^2`
If x + y + z = 12 and xy + yz + zx = 27; find x2 + y2 + z2.
Evaluate the following :
7.16 x 7.16 + 2.16 x 7.16 + 2.16 x 2.16
