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The value of will lie between
8 and 9
64 and 81
2 and 9
49 and 64
83 = 512 and 93 = 729
512 < 530 < 729
∴
Which of the following is not an identity
(x + y)3 = x3 + y3 + 3xy(x + y)
x3 + y3 = (x + y)(x2 − xy + y2)
(x − y)3 = x3 + y3 + 3xy(x − y)
x3 - y3 = (x - y)(x2 + xy + y2)
(x − y)3 = x3 - 3x2y + 3xy2 − y3
Factorise xy10z + xyz10.
xyz [(y3)3 + (z3)3]
xyz (y3+ z3) (y6 − y3z3 + z6)
xyz (x + z) (x2 − xz + z2) (y6 − y3z3 + z6)
(x2 − xy + y2) (y6 − y3z3 + z6)
xy10z + xyz10
= xyz (y9 + z9)
= xyz [(y3)3 + (z3)3]
Here, a = y3 and b = z3
= xyz (y3+ z3) [(y3)2 − y3z3 + (z3)2] ... using a3 + b3 = (a + b)(a2 − ab + b2)
= xyz (y3+ z3) (y6 − y3z3 + z6)
=xyz (x + z) (x2 − xz + z2) (y6 − y3z3 + z6) … using a3 + b3 = (a + b)(a2 − ab + b2)
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