Question

Factorise x³/8-64-3x²+24x by using suitable identity​

Answer 1

Answer:

Step-by-step explanation:

Check in the below attachment for the solution

Hope this helps you!

Answer 2

Factors are $\bf \frac{ {x}^{3} }{8} - 64 - 3 {x}^{2} + 24x = \left( { \frac{x}{2} - 4} \right)^{3}$

Given:

• $\frac{ {x}^{3} }{8} - 64 - 3 {x}^{2} + 24x$

To find:

• Factorise using suitable identity.

Solution:

Identity to be used:

$\bf ( {a - b)}^{3} = {a}^{3} - {b}^{3} - 3 {a}^{2} b + 3a {b}^{2}$

Step 1:

Rewrite the terms of given expression; so that identity can be applicable.

$\frac{ {x}^{3} }{8} - 64 - 3 {x}^{2} + 24x \\= \left( { \frac{x}{2} }\right)^{3} - ( {4)}^{3} - 3\left( { \frac{x}{2} }\right)^{2} \times 4 + 3 \times \frac{x}{2} \times {4}^{2}$

Step 2:

On comparison with the identity; It is clear that

$\bf a = \frac{x}{2}$

and

$\bf b = 4$

So,

$\frac{ {x}^{3} }{8} - 64 - 3 {x}^{2} + 24x = \left( { \frac{x}{2} - 4} \right)^{3}$

Thus,

Factors are $\bf \frac{ {x}^{3} }{8} - 64 - 3 {x}^{2} + 24x = \left( { \frac{x}{2} - 4} \right) \left( { \frac{x}{2} - 4} \right) \left( { \frac{x}{2} - 4} \right)$

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