Question

8 (a + b)^³ + 27 (b + c)^³
please factorise it and express it a sum or difference of two cubes, Answer is (2a + 5b + 3c)(4a² ± 7b² + 9c² ± 2ab + 12bc - 6ac), just answer the process involved in this, please don't spam, answer within 12 hours of this post, BTW good night. ​

Answer 1

Answer:

(2a + 5b + 3c)( 4a² + 7b² + 9c² + 2ab+ 12bc -6ac)

Step-by-step explanation:

There is a formula

a³ + b³ = (a+b)(a²- ab + b²)

Now getting back to the expression,

8 (a + b)³ + 27 (b + c)³

= 2³(a + b)³ + 3³(b + c)³

= (2a + 2b)^³ + (3b + 3c)³

Applying the above written formula,

= ( 2a + 2b + 3b + 3c)( [2a+2b]² -[2a + 2b][3b+ 3c] +[3b + 3c]²)

= (2a + 5b + 3c)( 4a² + 4b² + 8ab -6ab-6b²-6ac -6bc + 9b² + 9c² +18bc)

= (2a + 5b + 3c)( 4a² + 7b² + 9c² + 2ab+ 12bc -6ac)