Questions: Factor xy+8y-3x-24

Transcript text: Factor $x y+8 y-3 x-24$

Solution

Solution Steps

To factor the expression $xy + 8y - 3x - 24$, we can use the method of grouping. First, we group the terms in pairs and factor out the common factors from each pair. Then, we look for a common binomial factor in the resulting expression.

Step 1: Group the Terms

To factor the expression $xy + 8y - 3x - 24$, we start by grouping the terms in pairs: \[ (xy - 3x) + (8y - 24) \]

Step 2: Factor Out the Common Factors

Next, we factor out the common factors from each pair:

From the first pair $xy - 3x$, factor out $x$: \[ x(y - 3) \]
From the second pair $8y - 24$, factor out $8$: \[ 8(y - 3) \]

Step 3: Identify the Common Binomial Factor

Now, we observe that both terms have a common binomial factor $(y - 3)$: \[ x(y - 3) + 8(y - 3) \]

Step 4: Factor Out the Common Binomial

Factor out the common binomial $(y - 3)$: \[ (x + 8)(y - 3) \]

Final Answer

$\boxed{(x + 8)(y - 3)}$

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