Question

Which expression is equivalent to 2f-1/3(2g-3f)-1/3g?

Answer 1

The given expression is :

`2f-(1)/(3)(2g-3f)-(1)/(3)g`

Simplify by the BODMAS rule

B-Brackets, O- Of, D-Division, M-Multiplication, A-Add & S - SUbtract

Step 1 : Open the brackets

`2f-(1)/(3)(2g-3f)-(1)/(3)g=2f-(2)/(3)g+(3)/(3)f-(1)/(3)g`

Step 2 : Simplify the similar term together

`\begin{gathered} 2f-(1)/(3)(2g-3f)-(1)/(3)g=2f+(3)/(3)f-(1)/(3)g-(2)/(3)g \\ 2f-(1)/(3)(2g-3f)-(1)/(3)g=2f+f-(1)/(3)g-(2)/(3)g \\ 2f-(1)/(3)(2g-3f)-(1)/(3)g=f(2+1)-g((1)/(3)+(2)/(3)) \\ 2f-(1)/(3)(2g-3f)-(1)/(3)g=f(3)-g((3)/(3)) \\ 2f-(1)/(3)(2g-3f)-(1)/(3)g=f(3)-g(1) \\ 2f-(1)/(3)(2g-3f)-(1)/(3)g=3f-g \end{gathered}`

Answer : A) 3f - g