In the expansion of (2x 2 - 8)(x - 4) 2 ; find the value of : (i) coefficient of x 3 (ii) coefficient of x 2 (iii) constant term.

Given, ⇒ (2x 2 - 8)(x - 4) 2 Expanding, ⇒ (2x 2 - 8)(x 2 + 16 - 8x) ⇒ 2x 4 + 32x 2 - 16x 3 - 8x 2 - 128 + 64x ⇒ 2x 4 - 16x 3 + 24x 2 + 64x - 128. (i) Hence, coefficient of x 3 is -16. (ii) Hence, coefficient of x 2 is 24. (iii) Hence, constant term = -128.

Mathematics

In the expansion of (2x² - 8)(x - 4)²; find the value of :
(i) coefficient of x³
(ii) coefficient of x²
(iii) constant term.

Expansions

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Answer

Given,

⇒ (2x² - 8)(x - 4)²

Expanding,

⇒ (2x² - 8)(x² + 16 - 8x)

⇒ 2x⁴ + 32x² - 16x³ - 8x² - 128 + 64x

⇒ 2x⁴ - 16x³ + 24x² + 64x - 128.

(i) Hence, coefficient of x³ is -16.

(ii) Hence, coefficient of x² is 24.

(iii) Hence, constant term = -128.

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Mathematics

In the expansion of (2x2 - 8)(x - 4)2; find the value of :(i) coefficient of x3(ii) coefficient of x2(iii) constant term.

Expansions

Answer

Related Questions

In the expansion of (2x² - 8)(x - 4)²; find the value of :
(i) coefficient of x³
(ii) coefficient of x²
(iii) constant term.