Question

a3 -3a2b +3ab2 -2b3 factorise ​

Answer 1

Answer:

a³-3a²b+3ab²-b³

=a³-b³+3ab²-3a²b

=(a-b)(a²+ab+b²) -3ab(a-b)

=(a-b)(a²-3ab+ab+b²)

=(a-b)(a-b)²

=(a-b)³

THODA ATTACHMENT ME NAZAR DAAL DENA :) GUD NI8 XD XD

Answer 2

a³ -3a²b +3ab² -2b³ = (a - 2b)(a² + b² - ab)

Given:

• a³ -3a²b +3ab² -2b³

To Find:

• Factors

Solution:

Factorization is finding factors which when multiplied together results in the original number.

(x - y)³ = x³ - 3x²y  + 3xy² - y³

x³ - y³ = (x - y)(x² + y² +  xy)

(x - y)² = x² + y²  - 2xy

a³ -3a²b +3ab² -2b³

Step 1:

Rewrite -2b³ as -b³ - b³

a³ -3a²b +3ab² - b³ - b³

Step 2:

Use Identity (x - y)³ = x³ - 3x²y  + 3xy² - y³  where x = a , y =  b

( a - b)³ - b³

Step 3:

Use Identity x³ - y³ = (x - y)(x² + y² +  xy)  where x = (a-b) , y =  b

(a - b - b)((a - b)²  + b²  +(a-b)b)

Step 4:

Simplify using (x - y)² = x² + y²  - 2xy and distributive property and combining like terms

(a - b - b)(a² + b² - 2ab  + b²  + ab -  b²)

(a - 2b)(a² + b² - ab)

Hence a³ -3a²b +3ab² -2b³ = (a - 2b)(a² + b² - ab)