Question

simplify: $-3(y + 2)^2 - 5 + 6y$
what is the simplified product in standard form?
$\square y^2 + \square y + \square$

Explanation:

Step1: Expand the square term

First, we expand \((y + 2)^2\) using the formula \((a + b)^2 = a^2 + 2ab + b^2\). Here, \(a = y\) and \(b = 2\), so \((y + 2)^2 = y^2 + 4y + 4\). Then we multiply this by \(-3\):

$$ -3(y^2 + 4y + 4) = -3y^2 - 12y - 12 $$

Step2: Combine like terms

Now we substitute this back into the original expression and combine like terms. The original expression is \(-3(y + 2)^2 - 5 + 6y\), so substituting the expanded form we get:

$$ -3y^2 - 12y - 12 - 5 + 6y $$

Now combine the \(y\)-terms and the constant terms:

• For the \(y\)-terms: \(-12y + 6y = -6y\)
• For the constant terms: \(-12 - 5 = -17\)

So the simplified expression is:

$$ -3y^2 - 6y - 17 $$

Answer:

\(-3\) \(y^2+\) \(-6\) \(y+\) \(-17\) (Filling in the boxes: the coefficient of \(y^2\) is \(-3\), the coefficient of \(y\) is \(-6\), and the constant term is \(-17\))