Question

factorise (a+b)³-a-b​

Answer 1

How do we factorise [math]{(a+b)^3}{-a-b}[/math]?

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[math](a+b)^3-a-b=(a+b)^3-(a+b)[/math]

[math] [/math] =[math](a+b)[(a+b)^2-1][/math]

[math] =(a+b)[(a+b)^2-(1)^2][/math]

[math] =(a+b)(a+b+1)(a+b-1)[/math]

(a+b)^3-a-b

Factor out the negative sign

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

Factor out the (a+b) term

(a+b)[(a+b)^2–1]

Notice the difference of two squares (A^2-B^2 = (A+B)(A-B) where A = a+b, B = 1

(a+b)[(a+b)-1][(a+b)+1]

(a+b)(a+b-1)(a+b+1)