Question

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​

Answer 1

Step-by-step explanation:

Given that: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

To find: find the value of:(i) coefficient of x^3 (ii) coefficient of x^2 (iii) constant term

Solution:

To find the coefficient of given term,

Open the identity and expand the term

$\boxed{( {a - b)}^{2} = {a}^{2} - 2ab + {b}^{2}}$

apply this identity to open

$( {x - 4)}^{2} = {x}^{2} - 8x + 16$

Multiply this to first term

$( 2{x}^{2} - 8)( {x}^{2} - 8x + 16) \\ \\ = 2 {x}^{4} - 16 {x}^{3} + 32 {x}^{2} - 8 {x}^{2} + 64x - 128 \\ \\ ( 2{x}^{2} - 8)( {x}^{2} - 8x + 16)\\ = 2 {x}^{4} - 16 {x}^{3} + 24 {x}^{2} + 64x - 128$

Now,

Coefficient of x³ = -16

Coefficient of x² = 24

Constant term =-128

Hope it helps you.