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


User Nakul
by
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1 Answer

4 votes

Answer:


(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)

User Guilffer
by
8.0k points

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