Question

rene makes an error when she tries to write an expression equivalent to 12 + 15(3 - y) - 10y. what is the error? fix rene’s error.
12 + 15(3 - y) - 10y
12 + 45 + 15y - 10y
57 + 5y

Explanation:

Step1: Expand the original expression

First, we expand \(12 + 15(3 - y)-10y\) using the distributive property \(a(b - c)=ab - ac\). So, \(15(3 - y)=15\times3-15\times y = 45-15y\). Then the original expression becomes \(12 + 45-15y-10y\).

Step2: Identify Rene's error

Looking at Rene's expression (assuming the incorrect one is like \(12 + 45+15y - 10y\) or similar, from the given options), she made a mistake in the sign when distributing \(15\) over \((3 - y)\). She should have \( - 15y\) but likely used \(+15y\) instead.

Step3: Correct the expression

After expanding correctly, we combine like terms. First, combine the constant terms: \(12 + 45=57\). Then combine the \(y\)-terms: \(-15y-10y=-25y\). Wait, no, wait, let's re - do the expansion correctly. Wait, original expression: \(12+15(3 - y)-10y\). Distribute \(15\): \(15\times3 = 45\), \(15\times(-y)=-15y\). So the expression is \(12 + 45-15y-10y\). Now combine constants: \(12 + 45 = 57\), combine \(y\)-terms: \(-15y-10y=-25y\). But looking at the given expressions, maybe Rene's error was in the distribution of \(15\) over \((3 - y)\). If we take the correct expansion step, the correct expression after distributing is \(12 + 45-15y-10y\) (or further combining to \(57-25y\), but from the given options, let's check the steps.

Wait, the original problem's Rene's work: Let's assume the original expression is \(12 + 15(3 - y)-10y\). Rene's step: maybe she did \(15(3 - y)\) as \(45 + 15y\) instead of \(45-15y\). So the error is in the sign of the \(y\)-term when distributing. The correct distribution is \(15(3 - y)=45-15y\), so the expression becomes \(12 + 45-15y-10y\), and then combining like terms: \(12 + 45=57\), \(-15y-10y=-25y\), so the correct expression is \(57-25y\) or \(12 + 45-15y-10y\).

Answer:

Error: Rene made a sign error when distributing \(15\) over \((3 - y)\) (she used \(+15y\) instead of \(-15y\)).
Corrected expression: \(12 + 45-15y-10y\) (or further simplified to \(57 - 25y\))