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in Polynomials by (65.2k points)

Write the following cubes in expanded form : 

(i) (2x + 1)3 

(ii) (2a – 3b)3

(iii) [\(\frac{3}{2}\)x + 1]3

(iv) [x - \(\frac{2}{3}\)y]3

1 Answer

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by (65.5k points)
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Best answer

(i) (2x + 1)3

As per Identity,
(a + b)3 = a3 + b3 + 3ab(a + b)
(2x + 1)3 = (2x)3 + (1)3 + 3(2x)(1)(2x + 1)
= 8x3 + 1 + 6x(2x + 1)
= 8x3 + 1 + 12x2 + 6x
(2x + 1)3 = 8x3 + 12x2 + 6x + 1.

(ii) (2a – 3b)3
As per Identity,
(a – b)3 = a3 – b3 – 3ab(a – b)
(2a – 3b)3= (2a)3– (3b)3 – 3(2a)(3b)(2a-3b)
= 8a3 – 27b3 – 18ab(2a – 3b)
(2a – 3b)3= 8a3 – 27b3 – 36a2b + 54ab2

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