Find the value of a+b when \(\left(a^2+2ab+b^2\right)\left(a+b\right)=125\)
(a + b)(a + b) = (a)(a) + (a)(b) + (b)(a) + (b)(b) = a2 + ab + ab + b2 = a2 + 2ab + b2
So.... a2 + 2ab + b2 = (a + b)(a + b)
And if
(a2 + 2ab + b2)(a + b) = 125 then....
(a + b)(a + b)(a + b) = 125
(a + b)3 = 125
a + b = \(\sqrt[3]{125}\)
a + b = 5