Question

Multiply: (a+b),(a+b) and (a+b)​

Answer 1

Here,

`(a + b) [(a + b)(a + b)]`

`(a + b)( {a}^(2) + 2ab + {b}^(2) )`

`a( {a}^(2) + 2ab + {b}^(2) ) + b( {a}^(2) + 2ab + {b}^(2) )`

`{a}^(3) + {2a}^(2) b + {ab}^(2) + {a}^(2) b + {2ab}^(2) + {b}^(3)`

`{a}^(3) + 3 {a}^(2) b + {3ab}^(2) + {b}^(3)`

Thus,
`(a+b)^3=a^3+3a^2b+3ab^2+b^3`

Thus, in case of multiplication of a binomial or a trinomial by a binomial or a trinomial each term of the binomial or the trinomial should multiply each term of the given binomial or the trinomial and if needed, simplification should be performed.