Question

%20-%20%20%7Bb%7D%5E%7B2%7D%20%29" id="TexFormula1" title="( \frac{1}{2} {a}^{2} + \frac{1}{2} ab - {b}^{2} )" alt="( \frac{1}{2} {a}^{2} + \frac{1}{2} ab - {b}^{2} )" align="absmiddle" class="latex-formula">
​

Answer 1

Answer:

$\frac{1}{2}$ (a + 2b)(a - b)

Step-by-step explanation:

Assuming you require the expression to be factored

Given

$\frac{1}{2}$ a² + $\frac{1}{2}$ ab - b² ← factor out $\frac{1}{2}$ from each term

= $\frac{1}{2}$ (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

$\frac{1}{2}$ a² + $\frac{1}{2}$ ab - b² = $\frac{1}{2}$(a + 2b)(a - b)