Simplify the following:
(2x + 3y + 4z)(4x2 + 9y2 + 16z2 - 6xy - 12yz - 8zx)
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We know that (a + b + c)(a2 + b2 + c2 - ab - bc - ca) = a3 + b3 + c3 - 3abc
∴ The Given Expression = (2x + 3y + 4z)[(2x)2 + (3y)2 + (4z)2 - (2x)(3y) - (3y)(4z) - (4z)(2x)]
= (2x)3 + (3y)3 + (4z)3 - 3(2x)(3y)(4z)
= 8x3 + 27y3 + 64z3 - 72xyz
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(3p - 4q)(9p2 + 12pq + 16q2)
Find the product of the following:
(x + 1)(x + 2)(x + 3)
(x - 2)(x - 3)(x + 4)