Question

(a+b)³-(a-b)³ factories​

Answer 1

Step-by-step explanation:

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

= (a^3+3a^2b+3ab^2+b^3)-(a^3-3a^2b+3ab^2-b^3)

= 6a^2b+2b^3

=2b(3a^2+b^2)

If you are allowed complex coefficients this can be broken down into linear factors:

=2b(sqrt(3)a+ib)(sqrt(3)a-ib)

Notice also that:

(a+b)^3+(a-b)^3 = (b+a)^3-(b-a)^3 = 2a(3b^2+a^2)

Answer 2

Answer:

Expanding:

(a³ + 3a²b + 3ab² + b³) - (a³ - 3a²b + 3ab²-b³) -6a²b+2b²³

= 2b (3a² + b²)

If you are allowed complex coefficients this can

be broken down into linear factors:

= 2b(√3a + ib) (√3a - ib)

Notice also that:

(a + b)³ + (a−b)³ = (b + a)³ - (b − a)³

2a(36²+ a²)