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प्रश्न
Find the following product:
(2x – y + 3z)(4x2 + y2 + 9z2 + 2xy + 3yz – 6xz)
उत्तर १
(2x – y + 3z)(4x2 + y2 + 9z2 + 2xy + 3yz – 6xz)
= 2x(4x2 + y2 + 9z2 + 2xy + 3yz – 6xz) – y(4x2 + y2 + 9z2 + 2xy + 3yz – 6xz) + 3z(4x2 + y2 + 9z2 + 2xy + 3yz – 6xz)
= 8x3 + 2xy2 + 18xz2 + 4x2y + 6xyz – 12x2z – 4x2y – y3 – 9yz2 – 2xy2 – 3y2z + 6xyz + 12x2z + 3y2z + 27z3 + 6xyz + 9yz2 – 18xz2
= 8x3 + (2xy2 – 2xy2) + (18xz2 – 18xz2) + (4x2y – 4x2y) + (6xyz + 6xyz + 6xyz) + (–12x2z + 12x2z) – y3 + (–9yz2 + 9yz2) + (–3y2z + 3y2z) + 27z3
= 8x3 + 18xyz – y3 + 27z3
= 8x3 – y3 + 27z3 + 18xyz
उत्तर २
(2x – y + 3z)(4x2 + y2 + 9z2 + 2xy + 3yz – 6xz)
= (2x – y + 3z)[(2x)2 + (–y)2 + (3z)2 – (2x)(–y) – (–y)(3z) – (2x)(3z)]
= (2x)3 + (–y)3 + (3z)3 – 3(2x)(–y)(3z) ...[Using identity, (a + b + c)(a2 + b2 + c2 – ab – bc – ca) = a3 + b3 + c3 – 3abc]
= 8x3 – y3 + 27z3 + 18xyz
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