a)
Consider expression -4(r-3)+4r.
The above expression can be rewritten as,
[tex]\begin{gathered} -4(r-3)+4r=-4r-4\times(-3)+4r \\ =-4r+12+4r \\ =12 \end{gathered}[/tex]
Therefore, the equivalent expression of -4(r-3)+4r is 12.
b)
Consider expression 32w+6w+2.
This expression can be rewritten as,
[tex]\begin{gathered} 32w+6w+2=38w+2 \\ =2\times19w+2 \\ =2(19w+1) \end{gathered}[/tex]
Therefore, the equivalent expression of 32w+6w+2 is 2(19w+1).
c)
19w+2w-21
[tex]\begin{gathered} 19w+2w-21=21w-21 \\ =21(w-1) \end{gathered}[/tex]
Therefore, the equivalent expression of 19w+2w-21 is 21(w-1).
d)
6(k+10)+25+4k
[tex]\begin{gathered} 6\mleft(k+10\mright)+25+4k=6k+6\times10+25+4k \\ =6k+60+25+4k \\ =10k+85 \end{gathered}[/tex]
Therefore, the equivalent expression of 6(k+10)+25+4k is 10k+85.
e)
[tex]\begin{gathered} 12x^2+2x-6x^2-4x=12x^2-6x^2+2x-4x \\ =6x^2-2x \\ =2x\times3x^{}-2x \\ =2x(3x-1) \end{gathered}[/tex]
Therefore, the equivalent expression of
[tex]12x^2+2x-6x^2-4x[/tex]
is 2x(3x-1).
f)
6n+2+3n+16
[tex]\begin{gathered} 6n+2+3n+16=9n+18 \\ =9n+9\times2 \\ =9(n+2) \end{gathered}[/tex]
Therefore, the equivalent expression of 6n+2+3n+16 is 9(n+2).
