Question

If a-b=-10; ab = 16; find a³- b³​

Answer 1

Answer:

- 1480

Step-by-step explanation:

Given,

a - b = - 10

ab = 16

To find : a^3 - b^3 = ?

a^3 - b^3 = ( a - b )^3 + 3 ab ( a - b )

               = ( - 10 )^3 + 3 ( 16 ) ( - 10 )

               = - 1000 + 48 ( - 10 )

               = - 1000 - 480

a^3 - b^3 = - 1480

Answer 2

Given -

• a - b = - 10
• ab = 16

To find -

• a³- b³

Solution -

By using this identity -

$\LARGE{\boxed{\sf{\red{(a - b)^3 = a^3 - b^3 - 3ab(a - b)}}}}$

Substitute the given values.

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

$= \sf{( - 10)^3 = a^3 - b^3 - 3 \times 16( - 10)}$

$= \sf{- 1000 = a^3 - b^3 -48( - 10)}$

$= \sf{- 1000 = a^3 - b^3 + 480)}$

$= \sf{- 1000 - 480= a^3 - b^3}$

$= \sf{- 1480= a^3 - b^3}$

• a³- b³ = - 1480

━━━━━━━━━━━

Know more -

Some useful identities -

• $\sf\green{{(a - b)}^{2} = {a}^{2} + {b}^{2} - 2ab}$
• $\sf\green{{(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab}$
• $\sf\green{(a + b)^3 = a^3 + b^3 + 3ab(a + b)}$

Signs are changed on the following bases -

• (-) (-) = (+)
• (+) (+) = (+)
• (-) (+) = (-)
• (+) (-) = (-)