( (1)/(2) {a}^(2) + (1)/(2) ab - {b}^(2) ) ​

Question

`( (1)/(2) {a}^(2) + (1)/(2) ab - {b}^(2) )`
​

Answer 1

`(1)/(2)` (a + 2b)(a - b)

Explanation:

Assuming you require the expression to be factored

Given

`(1)/(2)` a² +
`(1)/(2)` ab - b² ← factor out
`(1)/(2)` from each term

=
`(1)/(2)` (a² + ab - 2b²) ← factor the quadratic

Consider the factors of the coefficient of the b² term(- 2) which sum to give the coefficient of the ab- term (+ 1)

The factors are + 2 and - 1, since

2 × - 1 = - 2 and 2 - 1 = + 1, thus

a² + ab - 2b² = (a + 2b)(a - b) and

`(1)/(2)` a² +
`(1)/(2)` ab - b² =
`(1)/(2)`(a + 2b)(a - b)