Question

find the value of a3-b3 for a =3 and b=-2​

Answer 1

Answer:

$a = 3 \\ b = - 2 \\ a {}^{3} - b {}^{3} \\ put \: values \: of \: a \: and \: b \: in \: formula \\ 3 {}^{3} - - 2 {}^{3} \\ 27 - { - 8} \\ 27 + 8 \\ 35 \\ hope \: it \: will \: help \: you$

Answer 2

Given :-

• Equation - a³ - b³
• a = 3
• b = ( - 2)

Have to Find :

• The value of a³ - b³

Solution :

We are going to use algebraic identity in order to get the value of the expression$.$

Identity Used :

• a³ - b³ → (a – b) (a² + b² + ab)

Now, we know a → 3 and b → (-2)

Substituting the values in it, we get

→ a³ - b³ = [ 3 - ( -2) ] [ (3)² + (-2)² + 3 × (-2) ]

→ a³ - b³ = 5 [ 9 + 4 - 6 ]

→ a³ - b³ = 5 [ 13 - 6 ]

→ a³ - b³ = 5 × 7

→ a³ - b³ = 35

.

Hence, the value of a³ - b³ is 35 .

_____________________________

Important Algebraic identities are:-

★ (a + b)² = a² + 2 ab + b²

 

★(a - b)² = (a + b)² - 4 ab

★ a² - b² = (a + b) (a - b)

 

★ (x + a) (x + b) =x² + (a + b) x + ab

★ (a + b)² = (a - b)² + 4 ab

★ (a - b)² = a² - 2 ab + b²

★ (a - b)³= a³- 3a²b + 3ab² - b³

★ (a - b)³ = a³- b³-3ab (a-b)

★ a³+ b³ = (a + b) (a²-ab + b²)

★ a³- b³= (a - b)(a²+ ab + b²)

★ a³- b³= (a - b)³ + 3ab(a-b)

★ (a + b + c)²= a²+ b²+ c² + 2ab + 2bc + 2ca

★ (a + b - c)² = a²+ b²+ c² + 2ab - 2bc -2ca

★ (a - b + c)²= a² + b²+c²-2ab -2bc +2ca

★ (a - b - c)²= a²+b²+c²-2ab +2bc -2ca

★a² + b² = (a - b)² + 2ab

★  (a + b + c)³ = a³ + b³ + c³ + 3a²b + 3a²c + 3ab²+3b²c + 3ac² + 3bc² + 6abc

★ (a - b - c)³ = a³ - b³ - c³ - 3a²b - 3a²c + 3ab² + 3b²c + 3ac² - 3bc² + 6abc