Question

Hello I just need you to show me how to do this

Answer 1

a)

Consider expression -4(r-3)+4r.

The above expression can be rewritten as,

`\begin{gathered} -4(r-3)+4r=-4r-4*(-3)+4r \\ =-4r+12+4r \\ =12 \end{gathered}`

Therefore, the equivalent expression of -4(r-3)+4r is 12.

b)

Consider expression 32w+6w+2.

This expression can be rewritten as,

`\begin{gathered} 32w+6w+2=38w+2 \\ =2*19w+2 \\ =2(19w+1) \end{gathered}`

Therefore, the equivalent expression of 32w+6w+2 is 2(19w+1).

c)

19w+2w-21

`\begin{gathered} 19w+2w-21=21w-21 \\ =21(w-1) \end{gathered}`

Therefore, the equivalent expression of 19w+2w-21 is 21(w-1).

d)

6(k+10)+25+4k

`\begin{gathered} 6\mleft(k+10\mright)+25+4k=6k+6*10+25+4k \\ =6k+60+25+4k \\ =10k+85 \end{gathered}`

Therefore, the equivalent expression of 6(k+10)+25+4k is 10k+85.

e)

`\begin{gathered} 12x^2+2x-6x^2-4x=12x^2-6x^2+2x-4x \\ =6x^2-2x \\ =2x*3x^{}-2x \\ =2x(3x-1) \end{gathered}`

Therefore, the equivalent expression of

`12x^2+2x-6x^2-4x`

is 2x(3x-1).

f)

6n+2+3n+16

`\begin{gathered} 6n+2+3n+16=9n+18 \\ =9n+9*2 \\ =9(n+2) \end{gathered}`

Therefore, the equivalent expression of 6n+2+3n+16 is 9(n+2).