Question

Priya rewrites the expression 8 − 24 as 8( − 3). Han rewrites 8 − 24 as2(4 − 12). Are Priya's and Han's expressions each equivalent to 8 − 24? Explain your reasoning.

Answer 1

The given expression is

$8y-24$

Priya rewrite the expression as

$8(y-3)$

Expanding priya's expression gives

$\begin{gathered} 8(y-3)=8\times y-8\times3 \\ 8(y-3)=8y-24 \end{gathered}$

Hence Priya's expression is equivalent to 8y - 24

Han's rewrite the expression as

$2(4y-12)$

Expanding Han's expression gives

$\begin{gathered} 2(4y-12)=2\times4y-2\times12 \\ 2(4y-12)=8y-24 \end{gathered}$

Hence, Han's expression is equivalent to 8y - 24