Question

Simplify the expression $a[b+c(ab+ac{)}^{\prime }]$

• A. $ac$
• B. $ab+c$
• C. $ab$
• D. $a^{\prime }b$

Answer 1

Answer: (C)

$ab$

$a[b+c{(ab+ac)}^{\prime }]=a[b+c{\left(ab\right)}^{\prime }{\left(ac\right)}^{\prime }]=a[b+c(a^{\prime }+b^{\prime })(a^{\prime }+c^{\prime })]=a[b+c(a^{\prime }+b^{\prime }{a}^{\prime }+a^{\prime }{c}^{\prime }+b^{\prime }{c}^{\prime })]=ab+ac{a}^{\prime }+ac{b}^{\prime }{a}^{\prime }+a{a}^{\prime }c{c}^{\prime }+a{b}^{\prime }c{c}^{\prime }=ab$