Question

if a- b = 8 and ab = - 12 then find a^3-b^3​

Answer 1

Step-by-step explanation:

ANSWER

Formula,

(a−b)

3

=a

3

−b

3

−3ab(a−b)

a−b=−8,ab=−12

a

3

−b

3

=(a−b)

3

+3ab(a−b)

=(−8)

3

+3(−12)(−8)=−224

Answer 2

Correct Question:

if a-b=-8,ab=-12 then find the value of a³-b³

Given:

a-b=-8

ab=-12

To Find :

value of a³-b³

$\huge\bold{\gray{\sf{Answer:}}}$

Explanation:

Here,this identity is used :-

$\bold{\boxed{\purple{ {(a - b)}^{3} = {a}^{3} - {b}^{3} - 3ab[a - b]}}}$

$= > {(a - b)}^{3} = {a}^{3} - {b}^{3} - 3ab(a - b)$

$= > {( - 8)}^{3} = {a}^{3} - {b}^{3} - 3 \times - 12( - 8)$

$= > {( - 8)}^{3} = {a}^{3} - {b}^{3} - 3 \times - 12( - 8)$

$= > - 512 = {a}^{3} - {b}^{3} - 288$

$= > - 512 + 288 = {a}^{3} - {b}^{3}$

$\bold{\boxed{ {a}^{3} - {b}^{3} = - 224}}$

Other Identity related to this :

$\bold{\boxed{ {(x -y)}^{2} = {x}^{2} + {y}^{2} - 2xy}}$

$\bold{\boxed{ {x}^{3} + {y}^{3} = {x}^{3} + {y}^{3} + 3xy(x + y)}}$

$\bold{\boxed{(x + y)(x + z) = {x}^{2} + (y+ z)x + yz}}$

$\bold{\boxed{ {(x +y)}^{3} = {x}^{3} + {y}^{3} +3xy[x+y]}}$