Which of the following is a factor of (x + y)3 - (x3 + y3)?
x2 + xy + 2xy
x2 + y2 - xy
xy2
3xy
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We know that,
(a + b)3 = a3 + b3 + 3ab(a + b).
∴ (x + y)3 - (x3 + y3) = x3 + y3 + 3xy(x + y) - x3 - y3 = 3xy(x + y).
Hence, Option 4 is the correct option.
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Factorisation of 16x2 + 40x + 25 is
(4x + 5)(4x + 5)
(4x + 5)(4x - 5)
(4x - 5)(4x - 5)
(4x + 5)(4x + 7)
Factorisation of x2 - 4xy + 4y2 is
(x + 2y)(x - 2y)
(x + 2y)(x + 2y)
(x - 2y)(x - 2y)
(2x - y)(2x + y)
If a + b + c = 0, then the value of a3 + b3 + c3 is
0
abc
2abc
3abc