Answer:
The equivalent expressions are:
[tex]4\left(4a+5\right)=16a+20[/tex]
[tex]=2\left(8a+10\right)[/tex]
[tex]=12a+20+4a[/tex]
Yes, 16a+20 could be further reduced by taking 2 as a common factor.
i.e. 16a+20 = 2(8a+10)
Step-by-step explanation:
Given the expression
solving the expression to determine the equivalent expression
[tex]4\left(4a+5\right)[/tex]
[tex]\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b+c\right)=ab+ac[/tex]
[tex]4\left(4a+5\right)=4\cdot \:\:4a+4\cdot \:\:5[/tex]
[tex]=16a+20[/tex]
Taking 2 as the common factor
[tex]=2\left(8a+10\right)[/tex]
Also
[tex]12a+20+4a = 16a+20[/tex]
Therefore, the equivalent expressions are:
[tex]4\left(4a+5\right)=16a+20[/tex]
[tex]=2\left(8a+10\right)[/tex]
[tex]=12a+20+4a[/tex]
Yes, 16a+20 could be further reduced by taking 2 as a common factor.
i.e. 16a+20 = 2(8a+10)
