Question

1. -18y - 27. the gcf of -18 and -27 is -9. -9 × □ = -18y -9 × □ = -27 the factored expression is □ 4. 28y - 32

Explanation:

For the expression \(-18y - 27\) (Problem 2):

Step 1: Find the first missing term

We know that \(-9 \times \text{(term)} = -18y\). To find the term, we divide \(-18y\) by \(-9\). So, \(\frac{-18y}{-9} = 2y\).

Step 2: Find the second missing term

We know that \(-9 \times \text{(term)} = -27\). To find the term, we divide \(-27\) by \(-9\). So, \(\frac{-27}{-9} = 3\).

Step 3: Write the factored expression

Using the distributive property \(ab + ac = a(b + c)\) (here \(a = -9\), \(b = 2y\), \(c = 3\)), the factored expression is \(-9(2y + 3)\).

For the expression \(28y - 32\) (Problem 4):

Step 1: Find the GCF of 28 and 32

First, factorize 28 and 32. The factors of 28 are \(1, 2, 4, 7, 14, 28\) and the factors of 32 are \(1, 2, 4, 8, 16, 32\). The greatest common factor (GCF) of 28 and 32 is 4.

Step 2: Factor out the GCF

We can write \(28y\) as \(4\times7y\) and \(-32\) as \(4\times(-8)\). Using the distributive property, \(28y - 32 = 4(7y - 8)\).

Answer:

s:

• For \(-9 \times \square = -18y\), the missing term is \(2y\).
• For \(-9 \times \square = -27\), the missing term is \(3\).
• The factored expression for \(-18y - 27\) is \(-9(2y + 3)\).
• The factored expression for \(28y - 32\) is \(4(7y - 8)\).