Find the product of the following:
(x + 1)(x + 2)(x + 3)
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We know that (x + a)(x + b)(x + c) = x3 + (a + b + c)x2 + (ab + bc + ca)x + abc
∴ (x + 1)(x + 2)(x + 3) = x3 + (1 + 2 + 3)x2 + [(1)(2) + (2)(3) + (3)(1)]x + (1)(2)(3)
= x3 + 6x2 + (2 + 6 + 3)x + 6
= x3 + 6x2 + 11x + 6
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Simplify the following:
(2x + 3y + 4z)(4x2 + 9y2 + 16z2 - 6xy - 12yz - 8zx)
(x - 2)(x - 3)(x + 4)
Find the coefficient of x2 and x in the product of (x - 3)(x + 7)(x - 4)