Question

question - 2 points written in factored form, the binomial $a^{2}b - ab^{2}$ is equivalent to (1) $ab(a - b)$ (2) $(a - b)(a + b)$ (3) $a^{2}(b - b^{2})$ (4) $a^{2}b^{2}(b - a)$

Explanation:

Step1: Factor out common terms

First, factor out the common - term \(ab\) from the binomial \(a^{2}b - ab^{2}\). We know that \(a^{2}b=ab\times a\) and \(ab^{2}=ab\times b\). So, \(a^{2}b - ab^{2}=ab(a - b)\) by the distributive property \(ac - bc=c(a - b)\) where \(c = ab\), \(a\) is replaced with \(a\) and \(b\) is replaced with \(b\).

Answer:

(1) \(ab(a - b)\)