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Question 6 of 8 , Step 1 of 1 Completely factor the expression by grouping, if possible. Correct \[ \text {. } \] Answer

Ask by Hodges Curry. in the United States
Feb 20,2025

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Please provide the expression you want to factor, and I will help you factor it by grouping.

Solución

To factor an expression by grouping, we typically follow these steps: 1. **Identify the expression**: We need to know the specific expression you want to factor. Please provide the expression you would like to factor. 2. **Group the terms**: If the expression has four or more terms, we can group them into pairs. 3. **Factor out the common factors**: For each group, factor out the greatest common factor (GCF). 4. **Look for a common binomial**: After factoring out the GCF from each group, check if there is a common binomial factor. 5. **Factor the common binomial**: If a common binomial factor exists, factor it out. Please provide the expression you want to factor, and I will guide you through the process step by step.

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The Deep Dive

When factoring by grouping, it's all about rearranging and regrouping terms to find common factors. For instance, if you have an expression like \( ax + ay + bx + by \), you can group them as \( (ax + ay) + (bx + by) \) and then factor out the common terms: \( a(x + y) + b(x + y) = (x + y)(a + b) \). This method works best when you have four terms, but don’t forget to check for any common factors in pairs or trios as well. If your expression is not factorable by grouping, you might need to look for other techniques like factoring by common factors or using the quadratic formula if you’re dealing with a quadratic expression. Happy factoring!

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