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प्रश्न
Factorise the following:
(x2 + y2 – z2)2 – 4x2y2
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उत्तर
(x2 + y2 – z2)2 – 4x2y2
= (x2 + y2 – z2)2 – (2xy)2
= (x2 + y2 – z2 – 2xy) (x2 + y2 – z2 + 2xy)
= [(x2 + y2 – 2xy) – z2] [(x2 + y2 + 2xy) – z2]
= [(x – y)2 – z2] [(x + y)2 – z2]
= [(x – y – z) (x – y + z)] [(x + y – z) (x + y + z)]
= (x – y – z) (x – y + z) (x + y – z) (x + y + z)
संबंधित प्रश्न
Factorise : 4xy - x2 - 4y2 + z2
Factorise : (x2 + 4y2 - 9z2)2 - 16x2y2
Factorise : a2 - b2 - (a + b) 2
Factorise : `4x^2 + 1/(4x)^2 + 1`
Factorise : 4x4 - x2 - 12x - 36
Factorise the following by the difference of two squares:
a(a - 1) - b(b - 1)
Factorise the following by the difference of two squares:
(x + y)2 -1
Factorise the following by the difference of two squares:
(x - 2y)2 -z2
Factorise the following:
4xy - x2 - 4y2 + z2
Factorise the following:
4x2 - 12ax - y2 - z2 - 2yz + 9a2
