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7 votes
7 votes
Find the term in x^7 in the expansion of (1 − x)^5 (3 + 2x)³

User Tien Hoang
by
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1 Answer

19 votes
19 votes

Answer:

4x^7

Explanation:

(1-x)³ (1-x)² (8x³ + 27 + 36x² + 54x)

(-x³+ 1 + 3x² - 3x) (x²+ 1 -2x) (8x³ + 27 + 36x² + 54x)

(-x^5 + 3x^4 - 3x³ + x² - x³ + 1 + 3x² - 3x + 2x^4 - 2x-6x³ +6x²) (8x³ + 27 + 36x² + 54x)

(-x^5 + 5x^4 -10x³ + 10x² -5x + 1) (8x³ + 27 + 36x² + 54x)


-8x^8 + 40x^7 - 80x^6 + 80x^5 - 40x^4 + 8x^3 - 27x^5 + 135x^4 -270x^3+ 270x^2- 135x + 27 - 36x^7+ 180x^6 - 360x^5 + 360x^4 - 180x^3 + 36x^2 - 54x^6 + 270x^5 - 540x^4 + 540x^3 - 270x^2 + 54x


27 - 81 x + 36 x^2 + 98 x^3 - 85 x^4 - 37 x^5 + 46 x^6 + 4 x^7 - 8 x^8

User Matheburg
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